existence and uniqueness of a nontrivial solution for a class of third order nonlinear p laplacian m point eigenvalue problems on time scales abstract in this paper we study the existence and uniqueness of a nontrivial solution for the following third order p laplacian m point eigenvalue problems on time scales p u f t u t u t 0 t 0 t u 0 u 0 0 u t i 1 m 2 a i u i u 0 0 where p s is p laplacian operator i e p s s p 2 s p 1 p 1 q 1 p 1 q 1 0 is a parameter 0 1 m 2 t we obtain several sufficient conditions of the existence and uniqueness of nontrivial solution of the above eigenvalue problems when is in some interval our approach is based on the leray schauder nonlinear alternative as an application some examples to demonstrate our results are given the conditions we used in the paper are different from those in z c hao l debnath on eigenvalue intervals and eigenfunctions of fourth order singular boundary value problems appl math lett 18 2005 543 553 d jiang r p agarwal a uniqueness and existence theorem for a singular third order boundary value problem on 0 1 appl math lett 15 2002 445 451 s h li positive solutions of nonlinear singular third order two point boundary value problem j math anal appl 323 2006 413 425 z liu j s ume d r anderson s m kang twin monotone positive solutions to a singular nonlinear third order differential equation j math anal appl 334 2007 299 313 q yao positive solutions to a special singular second order boundary value problem math comput model in press q yao successive iteration of positive solution for a discontinuous third order boundary value problem comput math appl 53 2007 741 749

multiple positive solutions for multipoint boundary value problems with one dimensional p laplacian abstract in this paper we consider the multiplicity of positive solutions for the one dimensional p laplacian differential equation p u q t f t u u 0 t 0 1 subject to some boundary conditions by means of a fixed point theorem due to avery and peterson we provide sufficient conditions for the existence of multiple positive solutions to some multipoint boundary value problems

a multi point boundary value problem with two critical conditions abstract we apply a coincidence degree theorem due to mawhin to show the existence of at least one solution of the nonlinear second order multi point boundary value problem u t f t u t u t t 0 1 u 0 u i 1 n i u i u 1 where 0 1 0 i 1 i 1 n i 1 n i i 1 n i i 1 n 2 and f 0 1 r 2 r satisfying the caratheodory conditions in our setting both boundary conditions are responsible for resonance

a fourth order compact finite difference method for nonlinear higher order multi point boundary value problems a fourth order compact finite difference method is proposed for a class of nonlinear 2nth order multi point boundary value problems the multi point boundary condition under consideration includes various commonly discussed boundary conditions such as the three or four point boundary condition n 2 point boundary condition and 2 n m point boundary condition the existence and uniqueness of the finite difference solution are investigated by the method of upper and lower solutions without any monotone requirement on the nonlinear term the convergence and the fourth order accuracy of the method are proved an efficient monotone iterative algorithm is developed for solving the resulting nonlinear finite difference systems various sufficient conditions for the construction of upper and lower solutions are obtained some applications and numerical results are given to demonstrate the high efficiency and advantages of this new approach

positive solutions for n order m point p laplacian operator singular boundary value problems in this paper we study the existence of positive solutions for the nonlinear n order m point p laplacian operator singular boundary value problems by using the method of defining operator by the reverse function of green function and the fixed point index theory the existence of positive solution and many positive solutions for nonlinear third order two point singular boundary value problem with p laplacian operator are obtained

a generalized multi point boundary value problem for second order ordinary differential equations let f 0 1 x r 2 r be a function satisfying caratheodory s conditions and e t l 1 0 1 let x i t j 0 1 a i b j r i 1 2 m 2 j 1 2 n 2 0 x 1 x 2 x m 2 1 0 t 1 t 2 t n 2 1 be given this paper is concerned with the problem of existence of a solution for the generalized multi point boundary value problems x t f t x t x t e t 0

multiple solutions and eigenvalues for third order right focal boundary value problems abstract we are concerned with the right focal boundary value problem x t f t x t t 1 t t 3 x t 1 x t 2 x t 3 0 and the associated eigenvalue problem x t a t f x t with the same boundary conditions under various assumptions on f a and we establish intervals of the parameter which yield the existence of a positive solution of the eigenvalue problem by placing certain restrictions on the nonlinearity we prove the existence of at least one at least two at least three and infinitely many positive solutions of the boundary value problem by applying some known fixed point theorems as well as some recent generalizations of these fixed point theorems

existence results for n point boundary value problem of second order ordinary differential equations abstract this study concerns the existence of positive solutions to the boundary value problem u a t f u 0 t 0 1 u 0 i 1 n 2 b i u i u 1 i 1 n 2 a i u i where i 0 1 with 0 1 2 n 2 1 a i b i 0 with 0 i 1 n 2 a i 1 and i 1 n 2 b i 1 by applying the krasnoselskii s fixed point theorem in banach spaces some sufficient conditions guaranteeing the existence of at least one positive solution or at least two positive solutions are established for the above general n point boundary value problem

multiple positive solutions of multi point boundary value problem for second order impulsive differential equations this paper is devoted to study the existence of multiple positive solutions for the second order multi point boundary value problem with impulse effects the arguments are based upon fixed point theorems in a cone an example is worked out to demonstrate the main results

three point boundary value problems for difference equations in this paper the existence and nonexistence of positive solutions for three point nonlinear boundary value problems of difference equations are considered

analysis of an infinite current source above a semi infinite lossy ground using fictitious current auxiliary sources in conjunction with complex image theory techniques the canonical problem of an infinitely long electric current line radiating above a lossy infinite half space is examined the solution is based on the method of auxiliary sources mas in this method one can in general apply a numerical solution by introducing sets of fictitious current sources whose fields are elementary analytical solutions to the boundary value problem in order to approximately describe the actual electromagnetic em fields in each domain in general the convergence rate and the accuracy of the mas solution depend on the spatial distributions of the fictitious current sources sets and their locations in regard to the singularities of the actual em field simulated by each set here both the accuracy and the convergence rate of the method are examined investigating complex image approximations in order to optimally choose the auxiliary sources placements it is proved that the convergence rate and the accuracy of the method are significantly improved by utilizing the complex images as locations of the auxiliary sources the main contribution of the paper consists in the application of mas to an open structure which involves lossy dielectrics excited by a nonuniform em field as well as in the optimal choice of the locations of the fictitious current sources according to complex image techniques

existence and iteration of positive solutions for a multipoint one dimensional p laplacian boundary value problem abstract in this paper we study the existence and iteration of positive solutions for the one dimensional p laplacian differential equation p u t q t f t u t u t 0 t 0 1 subject to the following multipoint boundary condition u 0 i 1 n 2 i u i u 1 i 1 n 2 i u i by applying a monotone iterative method we not only obtain the existence of positive solutions for the problem but also establish iterative schemes for approximating the solutions

global hypoellipticity of planar complex vector fields abstract we study the global hypoellipticity property for non singular planar complex vector fields the results obtained are related to condition p of nirenberg treves and the boundedness of certain subsets of the plane where the real and the imaginary parts of the vector field under consideration are linearly dependent we also prove the existence of a globally defined first integral when the vector field is globally hypoelliptic and has only one orbit

global properties of a class of vector fields in the plane on etudie l existence des solutions globales au probleme lu o du o sur r 2 ou l est un champ vectoriel sans singularite on se restreint au cas d operateurs localement integrables et satisfaisant certaines proprietes

triple positive solutions to third order three point bvp with increasing homeomorphism and positive homomorphism in this paper we investigate the existence of triple positive solutions for nonlinear differential equations boundary value problems with increasing homeomorphism and positive homomorphism operator by using fixed point theorems in cones we establish results on the existence of three positive solutions with suitable growth conditions imposed on the nonlinear term as applications two examples are given to demonstrate our result the conclusions in this paper essentially extend and improve the known results

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

successive iteration and positive symmetric solution for a sturm liouville like four point boundary value problem with a p laplacian operator abstract in this paper we consider the following sturm liouville like four point p laplacian boundary value problem with the nonlinear term f depending on the first order derivative p u t q t f t u t u t 0 0 t 1 subject to the boundary conditions u 0 u 0 u 1 u 0 by using a monotone iterative technique the existence of symmetric positive solutions and corresponding iterative schemes are obtained

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

green s function for a third order generalized right focal problem abstract we determine the green s function for the third order three point generalized right focal boundary value problem x t 0 t 1 t t 3 x t 1 x t 2 0 x t 3 x t 3 0 where 0 and determine conditions on the coefficients and boundary points to ensure its positivity then we use the krasnoselskii and leggett and williams fixed point theorems to prove the existence of solutions to the nonlinear problem x t f t x t t 1 t t 3 x t 1 x t 2 0 x t 3 x t 3 0 for certain constraints placed on nonnegative f

positive solutions for second order m point boundary value problems by using the schauder fixed point theorem and analysis method we establish the existence of solutions for the m point boundary value problem u t a t f u 0 u 0 0 u 1 i 1m 2kiu i b where b ki 0 i 1 2 m 2 0 b

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

solvability of an m point boundary value problem for second order ordinary differential equations let 0 1 r2 r be a function satisfying caratheodory s conditions and e t l1 0 1 let i 0 1 ai r all of the ai s having the same sign i 1 2 m 2 0 1 2 m 2 1 be given this paper is concerned with the problem of existence of a solution for the m point boundary value problem x t t x t x t e t t 0 1 e formula conditions for the existence of a solution for the above boundary value problem are given using the leray schauder continuation theorem

multiplicity results for singular conjugate focal and n p problems abstract a new technique is presented which enables us to discuss the existence of one or more solutions to singular conjugate focal and n p boundary value problems our nonlinearity f t y may be singular at y 0 t 0 and or t 1

on the phenomenon of oscillations in the method of auxiliary sources when one applies the method of auxiliary sources to scattering problems involving perfect conductors one first seeks fictitious auxiliary currents located inside the conductor and then determines the field from these currents for a simple two dimensional problem involving an infinite circular cylinder illuminated by an electric current filament it has recently been shown analytically that it is possible to have divergent auxiliary currents to make this statement precise one must properly normalize the currents together with a convergent field it was also shown through numerical investigations that the aforementioned divergence appears as abnormal rapid oscillations in the present paper we investigate such phenomena in more detail with particular emphasis on oscillations for a perfectly conducting ground plane illuminated by an electric current filament we once again demonstrate the possibility of having divergent oscillating currents producing a convergent field we develop an asymptotic formula for the oscillating current values which sheds light on the nature of the oscillations we revisit the circular cylinder problem to develop a similar asymptotic formula we also discuss roundoff errors and possible generalizations to scatterers of other shapes the present study is to a great extent analytical with the analytical predictions confirmed and supplemented by numerical results

multiple positive solutions for second order m point boundary value problems abstract in this paper the second order m point boundary value problem u t f t u 0 0 t 1 u 0 0 u 1 i 1 m 2 k i u i 0 is studied where k i 0 i 1 2 m 2 0 1 2 m 2 1 we give at first the associated green s function and its properties for the m point boundary value problem and growth conditions are imposed on f which yield the existence of at least three positive solutions by using the five functionals fixed point theorem and the properties

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

positive solutions of three point boundary value problems for systems of nonlinear second order ordinary differential equations abstract in this paper we study the three point boundary value problems for systems of nonlinear second order ordinary differential equations of the form u f t v t 0 1 v g t u t 0 1 u 0 v 0 0 u u 1 v v 1 under some conditions we show the existence and multiplicity of positive solutions of the above problem by applying the fixed point index theory 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

necessary and sufficient conditions for the existence of solution to three point bvp abstract we study the existence of a solution of the three point boundary value problem p x x g x h x 0 0 x x we give sufficient and necessary conditions on g and h in order for p to have a real solution our conditions are of landesman lazer type and depend on the real values of and

existence and iteration of positive solutions for a generalized right focal boundary value problem with p laplacian operator abstract in the paper we obtain the existence of positive solutions and establish a corresponding iterative scheme for the following third order generalized right focal boundary value problem with p laplacian operator p u t q t f t u t 0 t 1 u 0 i 1 m i u i u 0 u 1 i 1 n i u i the main tool is the monotone iterative technique

on the use of svd improved point matching in the current model method em scattering an approach which uses the singular value decomposition svd to improve the accuracy of the numerical solution obtained with fictitious current models is introduced in this approach the svd is essentially facilitating a systematic way to optimally reduce the generalized inverse matrix used in the solution to a submatrix of smaller rank this reduction strikes a balance between the fulfillment of the boundary conditions at the matching points and that between them clearly the boundary conditions errors at the matching points are no longer strictly zero however the previously discernible errors between the matching points are markedly suppressed the approach is efficacious not only when the impedance matrix is inherently singular or highly ill conditioned but also when this matrix is entirely well conditioned it can be generalized and implemented in any method of moments code which uses point matching for testing the approach has been incorporated into an existing solution based on the current model method for the problem of scattering from periodic sinusoidal surfaces and is shown to render the solution more accurate

analytic continuation considerations when using generalized formulations for scattering problems a generalized operator equation has been developed for a simple scattering problem for which a closed form solution exists the operator equation has been solved numerically via the method of moments using spatially impulsive fictitious sources as expansion functions together with a simple point matching testing procedure the study focused on the convergence and accuracy of the solution and examined how they are dependent on the location and distance of the fictitious sources relative to the area containing the singularities of the actual field simulated by these sources as expected it was found that when the actual field simulated by the fictitious impulsive sources has singularities lying between the physical boundary and the closed surface over which the sources are placed the impulsive expansion does not yield a uniformly convergent solution in this case instabilities are encountered as the number of sources increases in the sense that a small improvement of the boundary error requires a considerable change in the currents the moment matrix is then difficult to invert and easily susceptible to large round off errors conversely if the actual field has no singularities lying between the physical boundary and the closed surface over which the sources are placed the impulsive expansion does yield a uniformly convergent solution to any degree of precision

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 m point boundary value problems the second order m point boundary value problem x h x f x 0 0 x 1 0 0 1 i 1m 2ai i is considered under some conditions concerning the first eigenvalue of the relevant linear operator where i 0 1 with 0 1 2 m 2 1 ai 0 with i 1m 2ai 1 h x is allowed to be singular at x 0 and x 1 the existence of positive solutions and multiple positive solutions is obtained by means of fixed point index theory similarly conclusions hold for some other m point boundary value conditions

basis function considerations for the method of moments using the fictitious current model in the method of moments mom using the fictitious current model fcm an impulsive basis function is principally employed to expand the fictitious currents for various electromagnetic scattering problems in this paper we introduce the subdomain basis functions and consider the dependence of the solution accuracy and computation time of the mom fcm on the basis functions by means of a canonical two dimensional 2 d scattering problem

positive solutions of singular three point boundary value problems for second order differential equations in this paper we study the existence of positive solutions of a singular three point boundary value problem for the following second order differential equation y ma t f t y t 0 t 0 1 y 0 by 0 0 y 1 ay h where m 0 is a parameter b 0 0 0 by constructing an available integral operator and combining fixed point index theory with properties of green s function under some conditions concerning the first eigenvalues corresponding to the relevant linear operator the sufficient conditions of the existence of positive solutions for the boundary value problems are established the interesting point of the results is that the term a t may be singular at t 0 and or t 1 moreover the nonlinear f t x is also allowed to have singularity at x 0