existence and multiplicity results for a class of generalized one dimensional p laplacian problem abstract in this paper we study a class of one dimensional p laplacian boundary value problem with generalized sturm liouville boundary conditions some results are obtained for existence of at least three positive solutions by using the related fixed point theory the interesting point is the nonlinear term f which involves the first order derivative explicitly

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 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

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

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

existence and iteration of positive solutions for third order sturm liouville boundary value problems with p laplacian in this paper we investigate the existence and iteration of positive solutions for the following third order sturm liouville boundary value problem with p laplacian p u t q t f t u t u t 0 t 0 1 u 0 u 0 0 u 1 u 1 0 u 0 0 where p s s p 2 s p 1 by applying a monotone iterative technique we not only obtain the existence of positive solutions for the above boundary value problem but also establish iterative schemes for approximating the solutions

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

pattern based modeling and solution of probabilistically constrained optimization problems we propose a new modeling and solution method for probabilistically constrained optimization problems the methodology is based on the integration of the stochastic programming and combinatorial pattern recognition fields it permits the fast solution of stochastic optimization problems in which the random variables are represented by an extremely large number of scenarios the method involves the binarization of the probability distribution and the generation of a consistent partially defined boolean function pdbf representing the combination f p of the binarized probability distribution f and the enforced probability level p we show that the pdbf representing f p can be compactly extended as a disjunctive normal form dnf the dnf is a collection of combinatorial p patterns each defining sufficient conditions for a probabilistic constraint to hold we propose two linear programming formulations for the generation of p patterns that can be subsequently used to derive a linear programming inner approximation of the original stochastic problem a formulation allowing for the concurrent generation of a p pattern and the solution of the deterministic equivalent of the stochastic problem is also proposed the number of binary variables included in the deterministic equivalent formulation is not an increasing function of the number of scenarios used to represent uncertainty results show that large scale stochastic problems in which up to 50 000 scenarios are used to describe the stochastic variables can be consistently solved to optimality within a few seconds

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

existence and iteration of monotone positive solutions for multipoint boundary value problem with p laplacian operator in the paper we obtain the existence of monotone positive solutions and establish acorresponding iterative scheme for the following multipoint boundary value problem with p laplacian operator f p u t q t f t u t 0 0

multiple positive solutions for some p laplacian boundary value problems this paper deals with the existence of multiple positive solutions for the one dimensional p laplacian p x t q t f t x t x t 0 t 0 1 subject to one of the following boundary conditions p x 0 p x 0 0 p x 1 p x 1 0 or x 0 g1 x 0 0 x 1 g2 x 1 0 where p s s p 2s p 1 by means of a fixed point theorem due to avery and peterson sufficient conditions are obtained that guarantee the existence of at least three positive solutions the interesting point is the nonlinear term f is involved with the first order derivative explicitly

concavity and efficient points of discrete distributions in probabilistic programming we consider stochastic programming problems with probabilistic constraints involving integer valued random variables the concept of a p efficient point of a probability distribution is used to derive various equivalent problem formulations next we introduce the concept of r concave discrete probability distributions and analyse its relevance for problems under consideration these notions are used to derive lower and upper bounds for the optimal value of probabilistically constrained stochastic programming problems with discrete random variables the results are illustrated with numerical examples

triple positive solutions of a boundary value problem for nonlinear singular second order differential equations of mixed type with p laplacian in this paper we establish the existence of triple positive solutions of a two point boundary value problem for the nonlinear singular second order differential equations of mixed type with a p laplacian operator we also demonstrate that the results obtained can be applied to study certain higher order mixed boundary value problems finally an example is given to demonstrate the use of the main results of this paper

formability of linearly elastic structures with volume type actuation formation theory concerns the modification of the geometric configuration of an elastic structure by means of attached and or embedded actuators in this paper we consider volume type actuation which involves application of an isotropic expansive contractive stress to the elastic medium the question of formability i e whether or not a given modified geometric configuration for the elastic body can be achieved with actuation of this type is considered at length in both the two and three dimensional contexts along with related questions of optimal formability expressed in terms of the l 2 norm of the volume controller employed in two dimensions with the aid of the airy stress function we establish connections between optimal formation in the l 2 norm sense and the standard theory of conformal mapping of simply connected regions in the complex plane further results are presented for multiply connected domains including a complete discussion of the case of an annulus

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

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 f t u 0 t 0 1 subject to the boundary value condition u 0 i 1 n 2 i u i u 1 i 1 n 2 i u i where p s s p 2 s p 1 i 0 1 with 0 1 2 n 2 1 and i i satisfy i i 0 0 i 1 n 2 i 1 and i 1 n 2 i 1 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

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

multiple positive solutions for the one dimensional singular p laplacian we consider the following boundary value problem f p y q t f y 0 p 1 t 0 1 with y 0 y 1 0 or y 0 y 1 0 using a fixed point theorem for operators on a cone we provide sufficient conditions for the existence of multiple at least three positive solutions to the above boundary value problem an example is also included to illustrate the importance of the result obtained

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

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

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

eventual convexity of probability constraints with elliptical distributions probability constraints are often employed to intuitively define safety of given decisions in optimization problems they simply express that a given system of inequalities depending on a decision vector and a random vector is satisfied with high enough probability it is known that even if this system is convex in the decision vector the associated probability constraint is not convex in general in this paper we show that some degree of convexity is still preserved for the large class of elliptical random vectors encompassing for example gaussian or student random vectors more precisely our main result establishes that under mild assumptions eventual convexity holds i e the probability constraint is convex when the safety level is large enough we also provide tools to compute a concrete convexity certificate from nominal problem data our results are illustrated on several examples including the situation of polyhedral systems with random technology matrices and arbitrary covariance structure

three positive fixed points of nonlinear operators on ordered banach spaces we generalize the fixed point theorem of leggett williams which is a theorem giving conditions that imply the existence of three fixed points of an operator defined on a cone in a banach space we then show how to apply our theorem to prove the existence of three positive solutions to a second order discrete boundary value problem 2001 elsevier science ltd all rights reserved

solving chance constrained optimization problems with stochastic quadratic inequalities we propose a new and systematic reformulation and algorithmic approach to solve a complex class of stochastic programming problems involving a joint chance constraint with random technology matrix and stochastic quadratic inequalities the method is general enough to apply to nonconvex as well as nonseparable quadratic terms we derive two new reformulations and give sufficient conditions under which the reformulated problem is equivalent the second reformulation provides a much sparser representation of the feasible set of the chance constraint and offers tremendous computational advantages this new reformulation method can be used for linear stochastic inequalities and will also significantly improve the solution of such joint chance constrained problems we provide general and easily identifiable conditions under which the base reformulations can be linearized we show that the size of the reformulated problems in particular their number of binary variables and quadratic mixed integer terms does n

shape control by collinear actuators we consider a two dimensional elastic medium bounded by a free surface the medium deforms under the influence of actuators which are modelled as supplying a unidirectional stress the goal of the control mechanism provided by the actuators is to deform the body into a given shape in a linearized situation this means achieving a given normal displacement on the boundary we prove that for generic domains with smooth boundary every normal displacement of the boundary can be achieved we also consider stress free states for which the sum of the elastic stresses in the medium and the stress provided by the actuators vanishes the study of these states leads to a hyperbolic boundary value problem

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

multiple positive solutions for p laplacian equations with integral boundary conditions abstract in this paper we consider a class of boundary value problems for p laplacian equation p u h t f t u t u t 0 with integral boundary conditions u 0 u 0 0 1 g 1 s u s d s u 1 u 1 0 1 g 2 s u s d s by using the avery peterson fixed point theorem we obtain the existence of at least three positive solutions

erratum to threshold boolean form for joint probabilistic constraints with random technology matrix this note reports a correction and clarifies the results presented in 2 the third author of this corrigendum is not an author of the paper 2 in the original publication theorem 28 sect 4 2 1 p 410 states that the probabilistically constrained problem pmrtm can be reformulated as the quadratic integer optimization problem qde this statementmust be corrected since problemqde is in fact an inner approximation of the chance constrained problem pmrtm and the equivalence between qde and pmrtm can only be claimed under the specific settings presented below in the modified theorem 28 in part ii of theorem 28 in 2 p 411 it is shown that any feasible solution for the chance constrained problem pmrtm defined by a p sufficient recombination k is also feasible for the reformulated problem qde while that statement is correct this along with the fact any feasible solution of qde is feasible for pmrtm part

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

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

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

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

a formation problem in plane elasticity this article discusses modification of the shape of a plane elastic body whose uncontrolled geometric configuration is an annulus fixed along its interior boundary and free on its outer boundary the paper discusses the use of radial and circumferential actuators each of so called monotropic type to produce strictly radial deformations of the elastic structure so as to achieve target configurations or shapes in a specific class

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

existence of positive negative and sign changing periodic solutions for a class of integral equations in this paper the simultaneous existence of positive negative and sign changing periodic solutions for a class of integral equations of the form f x email protected x x w wk x y f y f email protected y dy email protected email protected is considered where w is a closed subset of r n with a periodic structure our main result is different from most existing results since they provide three constant sign periodic solutions only

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

threshold boolean form for joint probabilistic constraints with random technology matrix we develop a new modeling and solution method for stochastic programming problems that include a joint probabilistic constraint in which the multirow random technology matrix is discretely distributed we binarize the probability distribution of the random variables in such a way that we can extract a threshold partially defined boolean function pdbf representing the probabilistic constraint we then construct a tight threshold boolean minorant for the pdbf any separating structure of the tight threshold boolean minorant defines sufficient conditions for the satisfaction of the probabilistic constraint and takes the form of a system of linear constraints we use the separating structure to derive three new deterministic formulations for the studied stochastic problem and we derive a set of strengthening valid inequalities a crucial feature of the new integer formulations is that the number of integer variables does not depend on the number of scenarios used to represent uncertainty the computational study based on instances of the stochastic capital rationing problem shows that the mixed integer linear programming formulations are orders of magnitude faster to solve than the mixed integer nonlinear programming formulation the method integrating the valid inequalities in a branch and bound algorithm has the best performance