existence of solutions to k n k 2 boundary value problems we provide very general existence criteria to solutions for a class of higher order boundary value problems our results supplement as well as improve several recent results established in the literature

positive solutions of difference equations with two point right focal boundary conditions abstract we consider the following boundary value problem formula formula where 1 p n 1 is fixed using a fixed point theorem for operators on a cone we develop criteria for the existence of two positive solutions of the boundary value problem in addition upper and lower bounds for these positive solutions are established for special cases we also include several examples to dwell upon the importance of the results obtained

multiple nontrivial solutions for critical growth quasilinear elliptic systems abstract in the present paper we consider the following critical growth quasilinear elliptic system p u i 1 p d u i f u i u i q 2 u i in i 1 k u i 0 on i 1 k by exploiting the nehari manifold and variational methods we obtain the existence and multiplicity results of nontrivial solutions for the system

existence and nonexistence of solutions of second order nonlinear boundary value problems abstract we study the nonlinear boundary value problem consisting of the equation y q t y w t f y on a b and a general separated homogeneous linear boundary condition by comparing this problem with a corresponding linear sturm liouville problem we obtain conditions for the existence and nonexistence of solutions of this problem more specifically let n n 0 1 2 be the n th eigenvalues of the corresponding linear sturm liouville problem then under certain assumptions the boundary value problem has a solution with exactly n zeros in a b if n is in the interior of the range of f y y y 0 and does not have any solution with exactly n zeros in a b if n is outside of the range of f y y y 0 these conditions become necessary and sufficient when f y y is monotone the existences of multiple and even an infinite number of solutions are derived as consequences we also discuss the changes of the number and the types of nontrivial solutions as the interval a b shrinks as q increases in a given direction and as the boundary condition changes

positive periodic solutions for nonlinear difference equations with periodic coefficients abstract we prove the existence of positive solutions of second order nonlinear difference equations on a finite discrete segment with periodic boundary conditions obtained results yield positive periodic solutions of the equation on the whole discrete axis provided that the coefficients are periodic

existence and multiplicity of positive solutions to elliptic systems involving critical exponents abstract in this paper a singular elliptic system involving multiple critical exponents and the caffarelli kohn nirenberg inequality is investigated by using the extremals of the best hardy sobolev constants the existence and multiplicity of positive solutions to the system are established

upper estimate for positive solutions of the p n p conjugate boundary value problem abstract we consider the p n p conjugate boundary value problem a new upper estimate for positive solutions of the problem is obtained at the end of the paper we discuss the sharpness of this new upper estimate and a lower estimate from the literature

eigenvalues and eigenfunctions of discrete conjugate boundary value problems abstract we consider the following boundary value problem 1 n p n y f k y y n 1 y n 2 0 k m i y 0 0 0 i p 1 i y m n i 0 0 i n p 1 where 1 p n 1 is fixed and 0 a characterization of the values of is carried out so that the boundary value problem has a positive solution next for 1 criteria are developed for the existence of two positive solutions of the boundary value problem in addition for particular cases we also offer upper and lower bounds for these positive solutions several examples are included to dwell upon the importance of the results obtained

a generalization of concavity for finite differences abstract the concept of concavity is generalized to discrete functions u satisfying the n th order difference inequality 1 n k n u m 0 m 0 1 n and the homogeneous boundary conditions u 0 u k 1 0 u n k 1 u n n 0 for some k 1 n 1 a piecewise polynomial is constructed which bounds u below the piecewise polynomial is employed to obtain a positive lower bound on u m for m k n k where the lower bound is proportional to the supremum of u an analogous bound is obtained for a related green s function

three positive solutions for a nonlinear nth order m point boundary value problem abstract in this paper we consider the existence of at least three positive solutions for the nonlinear n th order m point boundary value problem u n t f t u 0 t 0 1 u 0 0 u 0 u n 2 0 0 u 1 i 1 m 2 k i u i where n 2 k i 0 i 1 2 m 2 0 1 2 m 2 1 the associated green s function for the n th order m point boundary value problem is first given and growth conditions are imposed on the nonlinearity f which yield the existence of multiple positive solutions by using the leggett williams fixed point theorem

singular nonlinear k n k conjugate boundary value problems abstract for 1 k n 1 solutions are obtained for the boundary value problem 1 n k y n f x y y i 0 0 0 i k 1 and y j 1 0 0 j n k 1 where f x y is singular at y 0 an application is made of a fixed point theorem for operators that are decreasing with respect to a cone

positive solutions of boundary value problems for disfocal ordinary differential equations we study the existence of positive solutions of a nonlinear eigenvalue problem for a two point boundary value problem for a family of second order disfocal ordinary differential equations we apply a cone theoretic fixed point theorem and obtain both sufficient conditions for the existence of positive solutions and sufficient conditions for the existence of multiple positive solutions

positive solutions for p n p conjugate boundary value problems a new existence result is presented for the p n p conjugate boundary value problem 1 n py n h t y 0 t 1 withy i 0 0 0 i p 1 andy i 1 0 0 i n p 1 our nonlinearityhmay be singular aty 0 t 0 and ort 1

general lidstone problems multiplicity and symmetry of solutions abstract for the 2mth order lidstone boundary value problem y 2 m t f y t y t y 2 i t y 2 m 1 t t 0 1 y 2 i 0 y 2 i 1 0 0 i m 1 where 1 mf r m 0 thinsp is continuous growth conditions are imposed on f which yield the existence of at least three symmetric positive solutions this generalizes earlier papers which have applied avery s generalization of the leggett williams theorem to lidstone problems we then prove the analogous result for difference equations

a three point boundary value problem for nonlinear fourth order differential equations abstract in this paper the authors consider the nonlinear fourth order ordinary differential equation e u t g t f u 0 with the boundary conditions b u 0 u 1 u 0 u p u 1 0 some results on the existence and nonexistence of positive solutions to problem e b are obtained results on the existence of infinitely many positive solutions are also presented examples are included to demonstrate that the results are sharp

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

multiple positive solutions for a critical elliptic system with concave convex nonlinearities we consider a semilinear elliptic system with both concave convex nonlinearities and critical growth terms in bounded domains the existence and multiplicity results of positive solutions are obtained by variational methods

three symmetric solutions of lidstone boundary value problems for difference and partial difference equations we consider the boundary value problem 2my k m f y k 2y k 1 2iy k 1 2 m 1 y k m 1 k a 1 b 1 2iy a 1 m 2iy b 1 m 2i 0 0 i m 1 where m 1 and 1 m f rm 0 is continuous by using amann and leggett williams fixed point theorems we develop growth conditions on f so that the boundary value problem has triple positive symmetric solutions the results obtained are then applied in the investigation of radial solutions for certain partial difference equation subject to lidstone type conditions

multiple positive solutions for semilinear elliptic systems abstract this article investigates the effect of the coefficient f z of the critical nonlinearity for sufficiently small 0 there are at least k positive solutions of the semilinear elliptic systems u g z u p 2 u f z u 2 u v in v h z v p 2 v f z u v 2 v in u v 0 on where 0 r n is a bounded domain 1 1 and 2 p 2 for n 4

several sufficient conditions of solvability for a nonlinear higher order three point boundary value problem on time scales abstract in this paper a nonlinear higher order three point boundary value problem on time scales is considered under certain growth conditions on the nonlinearity several sufficient conditions for the existence of nontrivial solution are obtained by using leray schauder nonlinear alternative as an application some examples to demonstrate our results are given

positive doubly periodic solutions of nonlinear telegraph equations abstract this paper deals with the existence of nontrivial doubly periodic solutions for the nonlinear telegraph equation u tt u xx cu t a t x u b t x f t x u t x r 2 where c 0 is a constant a b c r 2 r f c r 2 r r and a b f are 2 periodic in t and x we show the existence of positive doubly periodic weak solutions when 0 a t x c2 4 and f is either superlinear or sublinear on u by using the krasnoselskii s fixed point theorem in cones

hyperasymptotics for multidimensional integrals exact remainder terms and the global connection problem the method of steepest descents for single dimensional laplace type integrals involving an asymptotic parameter k was extended by berry howls in 1991 to provide exact remainder terms for truncated asymptotic expansions in terms of contributions from certain non local saddlepoints this led to an improved asymptotic expansion hyperasymptotics which gave exponentially accurate numerical and analytic results based on the topography of the saddle distribution in the single complex plane of the integrand in this paper we generalize these results to similar well behaved multidimensional integrands with quadratic critical points integrated over infinite complex domains as previously pointed out the extra complex dimensions give rise to interesting problems and phenomena first the conventionally defined surfaces of steepest descent are no longer unique second the stokes s phenomenon whereby contributions from subdominant saddles enter the asymptotic representation is of codimension one third we can collapse the representation of the integral onto a single complex plane with branch cuts at the images of critical points the new results here demonstrate that dimensionality only trivially affects the form of the exact multidimensional remainder thus the growth of the late terms in the expansion can be identified and a hyperasymptotic scheme implemented we show by a purely algebraic method how to determine which critical points contribute to the remainder and hence resolve the global connection problem riemann sheet structure and homology associated with the multidimensional topography of the integrand