positive solutions for higher order multi point boundary value problems with nonhomogeneous boundary conditions abstract we study nth order boundary value problems with a nonlinear term f t x subject to nonhomogeneous multi point boundary conditions criteria for the existence of positive solutions of such problems are established conditions are determined by the relationship between the behavior of f t x x near 0 and when compared with the smallest positive characteristic value of an associated linear integral operator this work improves and extends some recent results in the literature for the second order problems the results are illustrated with examples

positive solutions of nth order impulsive boundary value problems with integral boundary conditions in banach spaces abstract by using the fixed point theory for strict set contraction operator this paper investigates the existence of positive solutions for a class of n th order impulsive boundary value problems with integral boundary conditions in banach spaces moreover we offer some interesting discussion of the associated boundary value problems since the technique to deal with n th order bvp is completely different from that of previous papers the expression of the associated integral equation is simpler than that of relevant papers and upper and lower bounds for these positive solutions also are given our work is new

positive solutions of some singular m point boundary value problems at non resonance this paper investigates the existence of positive solutions for second order singular m point boundary value problems at non resonance a necessary and sufficient condition for the existence of c 0 1 as well as c 1 0 1 positive solutions is given by constructing lower and upper solutions and with the maximal theorem our nonlinearity f t x may be singular at x t 0 and or t 1

positive solutions for three point boundary value problems with dependence on the first order derivative abstract a new fixed point theorem in a cone is applied to obtain the existence of at least one positive solution for the second order three point boundary value problem x f t x x 0 0 x 0 0 x 1 x where f is a nonnegative continuous function 0 0 1

existence theorems for a second order three point boundary value problem abstract letf 0 1 r 2 r be continuous ande c 0 1 let i 0 1 ai r all of theai s having the same sign i 1 2 m 2 0 x t f t x t x t e t t 0 1 e x 0 0 x 1 i 1 m 2 a i x i bc m we discuss existence theorems for the problem e bcm under some sign condition offabout the origin our analysis is based on a nonlinear alternative of leray schauder

higher order boundary value problems with nonhomogeneous boundary conditions abstract we study the following nonlinear boundary value problem with nonhomogeneous multi point boundary condition u 2 n g t f t u t 0 1 u 2 i 0 j 1 m a j u 2 i t j 1 i 2 i u 2 i 1 j 1 m b j u 2 i t j 1 i 2 i 1 i 0 n 1 sufficient conditions are obtained for the problem to have at least one positive solution and to have no solution respectively moreover under certain conditions we prove that there exists a bounded and continuous surface separating r 2 n 0 0 into two disjoint subsets e and n with e such that the problem has at least two positive solutions for each 0 2 n 1 e one positive solution for each 0 2 n 1 and no positive solution for any 0 2 n 1 n

twin positive solutions for higher order m point boundary value problems with sign changing nonlinearities a new fixed point theorem on double cones is applied to obtain the existence of at least two positive solutions for the 2nd order m point boundary value problemy 2 n t f t y t y t y 2 n 1 t 0

sparse grid quadrature nonlinear filtering in this paper a novel nonlinear filter named sparse grid quadrature filter sgqf is proposed the filter utilizes weighted sparse grid quadrature points to approximate the multi dimensional integrals in the nonlinear bayesian estimation algorithm the locations and weights of the univariate quadrature points with a range of accuracy levels are determined by the moment matching method then the univariate quadrature point sets are extended to form a multi dimensional grid using the sparse grid theory compared with the conventional point based methods the estimation accuracy level of the sgqf can be flexibly controlled and the number of sparse grid quadrature points for the sgqf is a polynomial of the dimension of the system which alleviates the curse of dimensionality for high dimensional problems the unscented kalman filter ukf is proven to be a subset of the sgqf at the level 2 accuracy the performance of this filter is demonstrated by an orbit estimation problem the simulation results show that the sgqf achieves higher accuracy than the extended kalman filter ekf the ukf and the cubature kalman filter ckf in addition the sgqf is computationally much more efficient than the multi dimensional gauss hermite quadrature filter ghqf with the same performance

impulsive boundary value problems with integral boundary conditions and one dimensional p laplacian abstract by using the classical fixed point index theorem for compact maps some sufficient conditions for the existence of multiple positive solutions for a class of second order impulsive differential equations with p laplacian and integral boundary conditions are established which are the complement of previously known results meanwhile the existence of many solutions is also studied

optimal constants in a nonlocal boundary value problem we give improved results on the existence of positive solutions for a nonlinear differential equation with nonlocal boundary conditions that arise as a model of a thermostat we obtain some optimal criteria for the existence of one positive solution which involve the principal eigenvalue of a related linear operator we also determine optimal values of some other constants that are useful in obtaining existence of multiple positive solutions

local superlinearity for elliptic systems involving parameters abstract we study the existence non existence and multiplicity of positive solutions for a class of systems of second order ordinary differential equations using the fixed point theorem of cone expansion compression type the upper lower solutions method and degree arguments we apply our abstract results to study semilinear elliptic systems in bounded annular domains with non homogeneous boundary conditions here the nonlinearities satisfy local superlinear assumptions

positive solutions of nonlinear m point boundary value problems on time scales in this paper by using fixed point theorems in a cone and the associated green s function we study the existence of at least two and three positive solutions to the m point boundary value problem bvp on time scales u d t f t u t 0 email protected 0 1 t bu 0 email protected d 0 0 u 1 email protected email protected iu e i m 3 where t is a time scale email protected c l d 0 1 x 0 0 b email protected 0 a email protected 0 for i 1 2 m 2 and e i satisfy 0 e 1 e 2 e m 2 r 1

a numerical integration perspective on gaussian filters this paper proposes a numerical integration perspective on the gaussian filters a gaussian filter is approximation of the bayesian inference with the gaussian posterior probability density assumption being valid there exists a variation of gaussian filters in the literature that derived themselves from very different backgrounds from the numerical integration viewpoint various versions of gaussian filters are only distinctive from each other in their specific treatments of approximating the multiple statistical integrations a common base is provided for the first time to analyze and compare gaussian filters with respect to accuracy efficiency and stability factor this study is expected to facilitate the selection of appropriate gaussian filters in practice and to help design more efficient filters by employing better numerical integration methods

positive solutions of nonlinear second order m point boundary value problem abstract in this paper by using krasnoselskii s fixed point theorem of cone expansion compression type and under suitable conditions we present the existence of single and multiple positive solutions to the nonlinear second order m point boundary value problem u t a t f u t 0 0 t 1 u 0 0 u 1 i 1 m 2 a i u i where is a positive parameter a i 0 for i 1 2 m 3 and a m 2 0 i satisfy 0 1 2 m 2 1 and i 1 m 2 a i i 1 we derive an explicit interval of such that for any in this interval the existence of at least one positive solution to the boundary value problem is guaranteed and the existence of at least two solutions for in an appropriate interval is also discussed

multiple positive solutions for nonlinear singular m point boundary value problem abstract in this paper we study the existence of multiple positive solutions for the following nonlinear m point boundary value problem bvp u a t f u t 0 0 t 1 u 0 i 1 m 2 a i u i u 1 i 1 k b i u i i k 1 s b i u i i s 1 m 2 b i u i where r r is an increasing homeomorphism and homomorphism and 0 0 1 k s m 2 a i b i 0 with 0 i 1 k b i i k 1 s b i 1 0 i 1 m 2 a i 1 0 1 2 m 2 1 a t c 0 1 0 f c 0 0 some new results are obtained for the existence of at least twin or triple positive solutions of the above problem by applying avery henderson and a new fixed point theorems respectively as an application some examples are included to illustrate the main results in particular our results extend and improve some known results

multiple positive solutions for nth order m point boundary value problems with all derivatives abstract we investigate the existence of positive solutions for the boundary value problem u n t f t u t u t u n 2 t u n 1 t 0 0 t 1 u 0 u 0 u n 2 0 0 u n 1 1 i 1 m 2 k i u n 1 i where f 0 1 r n r is continuous k i 0 i 1 2 m 2 0 i 1 m 2 k i 1 we give at first the associated green s function and some of its properties then imposing growth conditions on f we obtain the existence of at least three positive solutions for the boundary value problem by using the five functional fixed point theorem finally we give an example to demonstrate our result

gaussian filters for nonlinear filtering problems we develop and analyze real time and accurate filters for nonlinear filtering problems based on the gaussian distributions we present the systematic formulation of gaussian filters and develop efficient and accurate numerical integration of the optimal filter we also discuss the mixed gaussian filters in which the conditional probability density is approximated by the sum of gaussian distributions a new update rule of weights for gaussian sum filters is proposed our numerical tests demonstrate that new filters significantly improve the extended kalman filter with no additional cost and the new gaussian sum filter has a nearly optimal performance

brief paper derivative free estimation methods new results and performance analysis the derivative free nonlinear estimation methods exploiting the stirling s interpolation and the unscented transformation for discrete time nonlinear stochastic systems are treated the divided difference and unscented filters smoothers and predictors based on the methods are introduced in the unified framework the new relations among the first order stirling s interpolation the second order stirling s interpolation and the unscented transformation are derived and their impact on the covariance matrices of the state estimates of the corresponding filters is analysed the theoretical results are illustrated and used for the explanation of the unexpected behaviour of the sigma point gaussian sum filters given as a mixture of the derivative free filters

solvability of a three point nonlinear boundary value problem for a second order ordinary differential equation in case f x u u ps x p x u pjx u with pk 0 l 4 r locally integrable the boundary value problem l lt 1 2 was studied by kiguradze and lomtatidze i the purpose of this paper is to obtain existence and uniqueness theorems for the boundary value problem 1 1 t 1 2 under natural conditions on f using degree theoretic arguments we note that if u is a solution of 1 1 1 2 then there exists at least one 5 e q l such that u c 0 accordingly the boundary value problem

riemann hilbert problems for the shapes formed by bodies dissolving melting and eroding in fluid flows the classical stefan problem involves the motion of boundaries during phase transition but this process can be greatly complicated by the presence of a fluid flow here we consider a body undergoing material loss due to either dissolution from molecular diffusion melting from thermodynamic phase change or erosion from fluid mechanical stresses in a fast flowing fluid in each case the task of finding the shape formed by the shrinking body can be posed as a singular riemann hilbert problem a class of exact solutions captures the rounded surfaces formed during dissolution melting as well as the angular features formed during erosion thus unifying these different physical processes under a common framework this study which merges boundary layer theory separated flow theory and riemann hilbert analysis represents a rare instance of an exactly solvable model for high speed fluid flows with free boundaries 2017 wiley periodicals inc

fully symmetric interpolatory rules for multiple integrals over hyper spherical surfaces fully symmetric interpolatory integration rules are constructed for multidimensional integrals over un the surface of an n dimensional hyper sphere explicit formulas for the weights are given for odd degrees 3 13 the new rules are efficient and only moderately unstable two randomization methods are described

positive solution of singular higher order m point boundary value problem with nonlinearity that changes sign this paper is about a class of singular higher order m point boundary value problems with nonlinearity that changes sign using the fixed point index theory we get a sufficient condition for the existence of positive solution to this problem

a general framework for solving riemann hilbert problems numerically a new numerical framework for the approximation of solutions to matrix valued riemann hilbert problems is developed based on a recent method for the homogeneous painleve ii riemann hilbert problem we demonstrate its effectiveness by computing solutions to other painleve transcendents an implementation in mathematica is made available online

method of riemann surfaces in the study of supercavitating flow around two hydrofoils in a channel abstract in the framework of the tulin model of supercavitating flow the problem of reconstructing the free surface of a channel and the shapes of the cavities behind two hydrofoils placed in an ideal fluid is solved in closed form the conformal map that transforms a parametric plane with three cuts along the real axis into the triple connected flow domain is found by quadratures the use of the theory of riemann surfaces the schottky doubles enables the non linear model problem to be reduced to two separate riemann hilbert problems on a hyperelliptic surface of genus two the solution to the first problem is a rational function with certain zeros and poles on a riemann surface the second problem is solved in terms of singular integrals with the weierstrass kernel the essential singularities of the solution at the infinite points of the surface due to a pole of the kernel are removed by solving a real analogue of the jacobi inversion problem on the surface the unknown parameters of the conformal map are recovered from a system of certain algebraic and transcendental equations

motion of a yawed supercavitating wedge beneath a free surface the problem that is studied concerns a yawed wedge under a free surface moving at a uniform speed the model involves a trailing cavity whose boundary is a dividing streamline through the vertex of the wedge the cavity closure mechanism is described according to the tulin terent ev single spiral vortex model a closed form solution to the governing nonlinear boundary value problem is found by the method of conformal mappings the doubly connected flow domain is treated as the image by this map of the exterior of two slits in a parametric plane the mapping function is constructed through the solution to two boundary value problems of the theory of analytic functions the hilbert problem for two slits in a plane and the riemann hilbert problem on an elliptic surface numerical results for the shape of the cavity and the free surface the yaw angle the drag and lift coefficients and the circulation are reported

single spiral vortex model for a cavitating elastic curvilinear foil a two dimensional nonlinear inverse fluid structure interaction problem for a curvilinear elastic hydrofoil is considered a cavity formed behind the foil is modeled according to the single spiral vortex model by tulin the fluid structure problem is decoupled by the method of successive approximations for the cavitation problem the foil is modeled as a polygon the method of conformal mappings and the riemann hilbert problem are employed at this stage the classical detachment mechanism for a smooth arc is satisfied for the polygon approximately the deformation of the smooth foil is described by the governing equations of the thin shell theory with the clamped clamped boundary conditions the loading acting on the middle surface of the foil is prescribed as the difference between the fluid and vapor pressure computed in the fluid problem numerical results include those for the cavity profile the drag coefficient the pressure distribution the speed and the displacements of the elastic foil

second order boundary value problems with nonhomogeneous boundary conditions ii sufficient conditions are given for the existence of solutions of the following nonlinear boundary value problem with nonhomogeneous multi point boundary condition u f t u u 0 t 0 1 u 0 i 1maiu ti 1 u 1 i 1mbiu ti 2 we prove that the whole plane r2 is divided by a continuous decreasing curve into two disjoint connected regions e and n such that the above problem has at least one solution for 1 2 has at least two solutions for 1 2 e and has no solution for 1 2 n we also find explicit subregions of e where the above problem has at least two solutions and two positive solutions respectively

a generalized traction integral equation for stokes flow with applications to near wall particle mobility and viscous erosion abstract a double layer integral equation for the surface tractions on a body moving in a viscous fluid is derived which allows for the incorporation of a background flow and or the presence of a plane wall the lorentz reciprocal theorem is used to link the surface tractions on the body to integrals involving the background velocity and stress fields on an imaginary bounding sphere or hemisphere for wall bounded flows the derivation requires the velocity and stress fields associated with numerous fundamental singularity solutions which we provide for free space and wall bounded domains two sample applications of the method are discussed we study the tractions on an ellipsoid moving near a plane wall which provides a more detailed understanding of the well studied glancing and reversing trajectories in the context of particle sedimentation and the erosion of bodies by a viscous flow in which the surface is ablated at a rate proportional to the local viscous shear stress simulations and analytical estimates suggest that a spherical body in a uniform flow first reduces nearly but not exactly to the drag minimizing profile and then vanishes in finite time the shape dynamics of an eroding body in a shear flow and near a wall are also investigated stagnation points on the body surface lead generically to the formation of cusps whose number depends on the flow configuration and or the presence of nearby boundaries

multiple positive solutions for m point boundary value problems with a one dimensional p laplacian abstract in this paper we consider the multipoint boundary value problem for the one dimensional p laplacian p u q t f t u 0 t 0 1 subject to the boundary conditions u 0 i 1 m 2 a i u i u 1 i 1 m 2 b i u i where p s s p 2 s by using a fixed point theorem in a cone we present sufficient conditions for the existence of multiple positive solutions for the above boundary value problem

on the existence of nonnegative solutions to an integral equation with applications to boundary value problems abstract by the use of a guo krasnoselskii theorem in cones existence of positive eigenvalues yielding nonnegative or positive solutions to an integral equation is studied the results are applied to a variety of boundary value problems concerning ordinary differential equations

a fast chebyshev method for simulating flexible wing propulsion abstract we develop a highly efficient numerical method to simulate small amplitude flapping propulsion by a flexible wing in a nearly inviscid fluid we allow the wing s elastic modulus and mass density to vary arbitrarily with an eye towards optimizing these distributions for propulsive performance the method to determine the wing kinematics is based on chebyshev collocation of the 1d beam equation as coupled to the surrounding 2d fluid flow through small amplitude analysis of the euler equations with trailing edge vortex shedding the complete hydrodynamics can be represented by a nonlocal operator that acts on the 1d wing kinematics a class of semi analytical solutions permits fast evaluation of this operator with o n log n operations where n is the number of collocation points on the wing this is in contrast to the minimum o n 2 cost of a direct 2d fluid solver the coupled wing fluid problem is thus recast as a pde with nonlocal operator which we solve using a preconditioned iterative method these techniques yield a solver of near optimal complexity o n log n allowing one to rapidly search the infinite dimensional parameter space of all possible material distributions and even perform optimization over this space

existence of triple positive solutions for multi point boundary value problems with a one dimensional p laplacian in this paper we consider the existence of multiple positive solutions for multi point boundary value problems with a one dimensional p laplacian f p u t q t f t u t u t 0 01 a email protected email protected i email protected email protected m 2 0 i 1 m email protected i i 1 m email protected email protected 0 1 0 x 1 x 2 x m 2 1 by the fixed point theorem due to avery and peterson we provide sufficient conditions for the existence of multiple positive solutions to the above boundary value problem

on positive solutions of an m point nonhomogeneous singular boundary value problem abstract this paper is concerned with the existence nonexistence and multiplicity of positive solutions for the following second order m point nonhomogeneous singular boundary value problem u t a t f t u 0 t 0 1 u 0 0 u 1 i 1 m 2 k i u i b where b 0 k i 0 i 1 2 m 2 0 1 2 m 2 1 i 1 m 2 k i i 1 a t may be singular at t 0 and or t 1 we show that under suitable conditions there exists a positive number b such that the above problem has at least two positive solutions for 0 b b at least one positive solution for b b and no solution for b b by using the krasnosel skii guo fixed point theorem the upper lower solutions method and topological degree theory

on the existence of positive solution for second order multi points boundary value problems here we are concerned with the existence of positive solution for autonomous and nonautonomous second order systems with multi points boundary conditions for nonautonomous systems we use the schauder s fixed point theorem in a suitable banach space while for autonomous ones using fixed point theorems is usually useless because of the existence of trivial solution and for this we employed a method based on the implicit function theorem and topological degree in order to verify the obtained results we have considered some definite systems to verify the results numerically

on numerical studies of multi point boundary value problem and its fold bifurcation based upon shooting method we set up a numerical method for approximating solutions and fold bifurcation solutions of second order multi point boundary value problems we prove the equivalence of the regularity of solutions and simple fold bifurcation solutions between the numerical method and the multi point boundary value problems many numerical experiments are carried out to illustrate the theoretical analysis from which we explore that the fold bifurcation phenomenon are generic in multi point boundary value problems although there is no theoretical analysis in the literature so far

a symmetric solution of a multipoint boundary value problem with one dimensional p laplacian at resonance abstract we apply an extension of mawhin s continuation theorem due to ge to show the existence of at least one symmetric solution of the multipoint boundary value problem for the one dimensional p laplacian at resonance p x t f t x t x t t 0 1 subject to the boundary conditions x 0 i 1 n i x i x 1 i 1 n i x i where p s s p 2 s p 1 0 1 2 n 1 2 i i 1 i 1 2 n i 1 n i 1 f 0 1 r 2 r with f t u v f 1 t u v for t u v 0 1 r 2 satisfying the caratheodory conditions

on the existence of positive solutions for semilinear elliptic equations in the annulus abstract we study the existence of positive radial solutions of u g x u 0 in annuli with dirichlet dirichlet neumann boundary conditions we prove that the problems have positive radial solutions on any annulus if is sublinear at 0 and

positive solutions for some second order four point boundary value problems abstract in this paper the second order four point boundary value problem x t h t f t x t 0 0 t 1 x 0 a x x 1 b x is studied where 0 1 0 a b 1 and h 0 1 0 f 0 1 0 0 are nonnegative continuous functions by the use of the property of the corresponding green s function fixed point index theory leray schauder degree and upper and lower solution method some existence nonexistence and multiplicity results of positive solutions are acquired

impulsive boundary value problems involving the one dimensional p laplacian abstract by using the classical fixed point index theorem for compact maps some sufficient conditions for the existence of multiple positive solutions for a class of second order impulsive differential equations with p laplacian are established which are complement of previously known results

existence of positive solution for singular semi positone k n k conjugate m point boundary value problem this paper is about a class of singular semi positone k n k conjugate m point boundary value problems by using the fixed point index theory we get a sufficient condition for the existence of positive solution to this problem

multiplicity of symmetric positive solutions for a multipoint boundary value problem with a one dimensional p laplacian abstract in this paper we consider the multipoint boundary value problem for the one dimensional p laplacian p u t q t f t u t u t 0 t 0 1 subject to the boundary conditions u 0 i 1 n i u i u 1 i 1 n i u i where p s s p 2 s p 1 i 0 0 i 1 n i 1 0 1 2 n 1 2 i i 1 i 1 2 n applying a fixed point theorem of functional type in a cone we study the existence of at least three symmetric positive solutions to the above boundary value problem the interesting point is that the nonlinear term f contains the first order derivative explicitly

global stability and decay for the classical stefan problem the classical one phase stefan problem describes the temperature distribution in a homogeneous medium undergoing a phase transition such as ice melting to water this is accom plished by solving the heat equation on a time dependent domain whose boundary is transported by the normal derivative of the temperature along the evolving and a priori unknown free boundary we establish a global in time stability result for nearly spherical geometries and small tempera tures using a novel hybrid methodology which combines energy estimates decay estimates and hopf type inequalities 1 1 the problem formulation we consider the problem of global existence and asymptotic stability of classical solutions to the classical stefan problem describing the evolving free boundary between the liquid and solid phases the temperature of the liquid p t x and the a priori unknown moving phase boundary t must satisfy the following system of equations

existence of three positive solutions for m point boundary value problems with one dimensional p laplacian abstract in this paper we consider the multipoint boundary value problem for the one dimensional p laplacian p u q t f t u t u t 0 t 0 1 subject to the boundary conditions u 0 0 u 1 i 1 m 2 a i u i where p s s p 2 s p 1 i 0 1 with 0 1 2 m 2 1 and a i 0 1 0 i 1 m 2 a i 1 using a fixed point theorem due to avery and peterson we study the existence of at least three positive solutions to the above boundary value problem the interesting point is that the nonlinear term f explicitly involves a first order derivative

multiple positive solutions for multipoint boundary value problems with sign changing nonlinearity abstract in this paper we consider the multipoint boundary value problem for one dimensional p laplacian p u q t f t u 0 t 0 1 subject to the boundary value conditions u 0 i 1 n i u i u 1 i 1 n i u i where p s s p 2s p 1 i 0 1 with 0 1 2 n 1 and i i 0 satisfy 0 i 1 n i i 1 n i 1 the nonlinear term f may change sign using a fixed point theorem for operators in a cone we provide sufficient conditions for the existence of multiple positive solutions to the above boundary value problem

nonlinear steepest descent and numerical solution of riemann hilbert problems the effective and efficient numerical solution of riemann hilbert problems has been demonstrated in recent work with the aid of ideas from the method of nonlinear steepest descent for riemann hilbert problems the resulting numerical methods have been shown in practice to retain accuracy as values of certain parameters become arbitrarily large remarkably this numerical approach does not require knowledge of local parametrices rather the deformed contour is scaled near stationary points at a specific rate the primary aim of this paper is to prove that this observed asymptotic accuracy is indeed achieved to do so we first construct a general theoretical framework for the numerical solution of riemann hilbert problems second we demonstrate the precise link between nonlinear steepest descent and the success of numerics in asymptotic regimes in particular we prove sufficient conditions for numerical methods to retain accuracy finally we compute solutions to the homogeneous painleve ii equation and the modified korteweg de vries equation to explicitly demonstrate the practical validity of the theory 2014 wiley periodicals inc

a new method for the nonlinear transformation of means and covariances in filters and estimators this paper describes a new approach for generalizing the kalman filter to nonlinear systems a set of samples are used to parametrize the mean and covariance of a not necessarily gaussian probability distribution the method yields a filter that is more accurate than an extended kalman filter ekf and easier to implement than an ekf or a gauss second order filter its effectiveness is demonstrated using an example

existence of two solutions of m point boundary value problem for second order dynamic equations on time scales in this paper by means of a new twin fixed point theorem in a cone the existence of at least two positive solutions of m point boundary value problem for second order dynamic equations on time scales is considered

existence of positive solutions to n point nonhomogeneous boundary value problem in this paper we are concerned with the existence of positive solutions to a n point nonhomogeneous boundary value problem by using the krasnoselskii s fixed point theorem in banach spaces some sufficient conditions guaranteeing the existence of positive solution is established for the n point nonhomogeneous boundary value problem

a sharper condition for the solvability of a three point second order boundary value problem letf 0 1 r2 rbe a function satisfying caratheodory s conditions ande t l1 0 1 let 0 1 r 1 1 be given this paper is concerned with the problem of existence of a solution for the three point boundary value problem formula omitted this problem was studied earlier by gupta ntouyas and tsamatos when 1 and when 1 with 1 in the general case this problem was studied by gupta as a multi point boundary value problem in this paper sharper existence conditions are obtained for the solvability of the above boundary value problem in the general case

double cavity flow past a wedge a mathematical model of supercavitating flow past a wedge with sides of arbitrary length is proposed the flow branches at a point on the lower side of the wedge at the vertex of the wedge and at the ends of the wedge the flow breaks away forming a nose bubble and a trailing cavity the closure mechanism is described by the tulin single spiral vortex model the flow domain is mapped into a parametric plane cut along a unit segment the conformal mapping function is reconstructed through the exact solution of two riemann hilbert problems on a genus zero riemann surface to complete the solution one needs to determine five real parameters from a certain system of transcendental equations numerical results are presented for the case when a wedge can rotate about the vertex in the flow domain in this case the flow branches at the vertex and the number of the parameters to be determined is 3

new developments in state estimation for nonlinear systems based on an interpolation formula accurate state estimators for nonlinear systems can be derived the estimators do not require derivative information which makes them simple to implement

cubature kalman smoothers the cubature kalman filter ckf is a relatively new addition to derivative free approximate bayesian filters built under the gaussian assumption this paper extends the ckf theory to address nonlinear smoothing problems the resulting state estimator is named the fixed interval cubature kalman smoother fi cks moreover the fi cks is reformulated to propagate the square root error covariances although algebraically equivalent to the fi cks the square root variant ensures reliable implementation when committed to embedded systems with fixed precision or when the inference problem itself is ill conditioned finally to validate the formulation the square root fi cks is applied to track a ballistic target on reentry

on an m point boundary value problem for second order ordinary differential equations where q e 0 1 is given we obtain conditions for the existence and uniqueness of a solution for the boundary value problem 2 using the leray schauder continuation theorem 2 we give an example of a three point boundary value problem where the existence condition is not satisfied and no solution exists gupta 3 recently studied the boundary value problem 2 when q 1 our results on the three point boundary value problem 2 extend the results of gupta 3 to the case of general cy see also 4 51 we use the classical spaces c o 11 c o 11 lk o 11 and l o l of continuous k times continuously differentiable measurable real valued functions whose kth power of the absolute value is lebesgue integrable on 0 11 or measurable functions that are essentially bounded

loss of positivity in a nonlinear second order ordinary differential equations we consider existence of nonzero solutions to the following boundary value problem u t f t u 0 t 0 1 u 0 u u 1 u 0 where and are positive parameters 0 1 we prove that solutions lose positivity as the parameter or increases in particular we study problems where the associated integral equation has a kernel that changes sign the proof is based on the fixed point theorem in cones

existence of multiple positive solutions for multipoint boundary value problems with a one dimensional p laplacian abstract in this paper we consider the multipoint boundary value problem for a one dimensional p laplacian p u a t f t u 0 t 0 1 u 0 0 u 1 i 1 m 2 a i u i where p s s p 2 s p 1 0 1 2 m 2 1 a i 0 for i 1 2 m 3 and a m 2 0 using a fixed point theorem for operators on a cone we provide sufficient conditions for the existence of multiple positive solutions to the above boundary value problem

green s function and positive solutions of nth order m point boundary value problem abstract in this paper we study the expression and properties of green s function for nth order m point boundary value problem u n t a t f u 0 t 0 1 u 0 u 0 u n 2 0 0 u 1 i 1 m 2 i u i where 0 0 with i 1 m 2 i i n 1 1 furthermore we obtained the existence of positive solutions by meas of fixed point index theory

positive solutions of a nonlinear m point boundary value problem let ai 0 for i 1 m 3 and am 2 0 let i satisfy 0 1 2 m 2 1 and m 2i 1 ai i 1 we study the existence of positive solutions to the boundary value problem where a c 0 1 0 and f c 0 0 we show the existence of at least one positive solution if f is either superlinear or sublinear by applying a fixed point theorem in cones

cubature kalman filters in this paper we present a new nonlinear filter for high dimensional state estimation which we have named the cubature kalman filter ckf the heart of the ckf is a spherical radial cubature rule which makes it possible to numerically compute multivariate moment integrals encountered in the nonlinear bayesian filter specifically we derive a third degree spherical radial cubature rule that provides a set of cubature points scaling linearly with the state vector dimension the ckf may therefore provide a systematic solution for high dimensional nonlinear filtering problems the paper also includes the derivation of a square root version of the ckf for improved numerical stability the ckf is tested experimentally in two nonlinear state estimation problems in the first problem the proposed cubature rule is used to compute the second order statistics of a nonlinearly transformed gaussian random variable the second problem addresses the use of the ckf for tracking a maneuvering aircraft the results of both experiments demonstrate the improved performance of the ckf over conventional nonlinear filters

the existence of solutions to second order singular boundary value problems abstract this article analyzes qualitative properties of solutions to two point boundary value problems for singular ordinary differential equations in particular we form new approaches that ensure that all possible solutions satisfy certain a priori bounds the methods involve differential inequalities the ideas are then applied to generate new existence results for solutions to the boundary value problems under consideration many of the results are novel for both the singular and the nonsingular cases the main concepts are further illustrated via applications to various equations arising in modeling such as the poisson boltzmann equation and the thomas fermi equation with an ionized atom

positive solutions for multipoint boundary value problems with one dimensional p laplacian operator in this paper we study the existence of positive solutions for the following nonlinear m point boundary value problem with p laplacian p u a t f u t 0 0 t 1 u 0 i 1m 2aiu i u 1 i 1kbiu i i k 1sbiu i i s 1m 2biu i where p s is p laplacian operator i e p s s p 2s p 1 q p 1 1p 1q 1 1 k s m 2 ai bi 0 with 0 i 1kbi i k 1sbi 1 0 i 1m 2ai 1 0 1 2 m 2 1 a t c 0 1 0 f c 0 0 we show that there exists one or two positive solutions by using fixed point theorem for operator on a cone the conclusions in this paper essentially extend and improve the known results

high degree cubature kalman filter the cubature kalman filter ckf which is based on the third degree spherical radial cubature rule is numerically more stable than the unscented kalman filter ukf but less accurate than the gauss hermite quadrature filter ghqf to improve the performance of the ckf a new class of ckfs with arbitrary degrees of accuracy in computing the spherical and radial integrals is proposed the third degree ckf is a special case of the class the high degree ckfs of the class can achieve the accuracy and stability performances close to those of the ghqf but at lower computational cost a numerical integration problem and a target tracking problem are utilized to demonstrate the necessity of using the high degree cubature rules to improve the performance the target tracking simulation shows that the fifth degree ckf can achieve higher accuracy than the extended kalman filter the ukf the third degree ckf and the particle filter and is computationally much more efficient than the ghqf

ideal free streamline flow over a curved obstacle in the classical two dimensional model the description of helmholtz s kirchhoff flow is a problem of complex analysis which can be solved analytically only for a few simple bodies or polygonal contours using the schwarz christoffel map this paper presents a practical method for computing flows over arbitrary obstacles whose boundaries may be piecewise smooth curves while the impinging flow may be an unbounded flow a jet or a semi infinite stream i e the ocean

existence of multiple positive solutions for nonlinear m point boundary value problems abstract in this paper we afford some sufficient conditions to guarantee the existence of multiple positive solutions for the nonlinear m point boundary value problem for the one dimensional p laplacian p u a t f t u 0 t 0 1 u 0 0 u 1 i 1 m 2 a i u i

positive solutions for nonhomogeneous m point boundary value problems let a c 0 1 b c 0 1 0 let d r and d 0 let 1 t be the unique solution of the linear boundary value problem u t a t u t b t u t 0 t 0 1 u 0 0 u 1 1 we study the existence of positive solutions for the m point boundary value problem u a t u t b t u h t f u 0 u 0 0 u 1 i 1m 2 iu ei d where i 0 1 and i 0 for i 1 m 2 are given constants satisfying i 1m 2 ix 1 d

positive solutions of nonlinear third order m point bvp for an increasing homeomorphism and homomorphism with sign changing nonlinearity in this paper several existence theorems of positive solutions are established for a nonlinear m point boundary value problem for the following third order differential equations f u a t f t u t 0 email protected 0 1 f u 0 email protected i 1m 2a email protected u x i u 0 0 u 1 email protected i 1m 2b iu x i where f email protected r is an increasing homeomorphism and homomorphism and f 0 0 the nonlinear term f may change sign as an application an example to demonstrate our results is given

positive solutions of an m point boundary value problem with sign changing nonlinearities let a i 0 for i 1 m 2 let x i satisfy 0 x 0 x 1 x 2 x m 2 x m 1 1 and m 2 i 1a email protected i 1 we study the existence of positive solutions to the boundary value problem u f t u 0 0

on the existence of positive solution for a kind of multi point boundary value problem at resonance abstract this paper concerns the existence of positive solution for a class of second order m point boundary value problems under different resonant conditions by using the leggett williams norm type theorem due to o regan and zima we obtain the existence of positive solution an example is given to demonstrate the main results

positive solutions of nonlinear three point boundary value problems abstract let a c 0 1 b c 0 1 0 let 1 t be the unique solution of the linear boundary value problem u t a t u t b t u t 0 t 0 1 u 0 0 u 1 1 we study the existence of positive solutions to the nonlinear boundary value problem u t a t u t b t u t h t f u 0 t 0 1 u 0 0 u u 1 where 0 0 and f c 0 0 we show the existence of at least one positive solution if f is either superlinear or sublinear by applying the fixed point theorem in cones

monotone positive solutions of second order multi point boundary value problems abstract in this paper by using guo krasnosel skii fixed point theorem and schauder s fixed point theorem we establish sufficient conditions for the existence and nonexistence of monotone increasing positive solution for a class of second order differential equation with multi point nonhomogeneous boundary conditions

relations between sparse grid quadrature rule and spherical radial cubature rule in nonlinear gaussian estimation the recently emerging cubature kalman filter and the sparse grid quadrature filter approximate the numerical integrations for the mean and covariance in gaussian filters using the spherical radial cubature rule and the sparse grid quadrature rule respectively this technical note reveals that 1 spherical rules can be obtained by the projection of sparse grid quadrature rules 2 the third and some of the fifth degree spherical radial cubature rules can be directly constructed from sparse grid quadrature rules