systems of first order impulsive functional differential equations with deviating arguments and nonlinear boundary conditions abstract this paper is concerned with the existence of solutions for systems of first order impulsive functional differential equations with deviating arguments and nonlinear boundary conditions by establishing new comparison results and applying the monotone iterative technique we obtain the sufficient conditions for the existence of extremal system of solutions

boundary value problem for first order impulsive functional integro differential equations this paper investigates extremal solutions of the boundary value problem for impulsive functional integro differential equations with nonlinear boundary conditions and deviating arguments in the presence of a lower solution u and an upper solution v with u v existence of extremal solutions is proved by establishing a new comparison principle and using the monotone iterative technique

existence and uniqueness of solutions of second order three point boundary value problems with upper and lower solutions in the reversed order abstract this paper studies the existence and uniqueness of solutions of second order three point boundary value problems with lower and upper solutions in the reversed order obtains the sufficient conditions for the existence and uniqueness of solutions by use of the monotone iterative method and gives the iterative sequence for solving a solution and its error estimate formula under the condition of unique solution

existence theorems for second order discrete boundary value problems abstract this article is concerned with the existence of solutions of boundary value problems for nonlinear second order difference equations of the type p n x n 1 q n x n f n x n where 0 is the ratio of odd positive integers p n and q n are real sequences the authors apply the linking theorem and the mountain pass lemma in the critical point theory and give some new results for the existence of solutions

monotone iterative method for the second order three point boundary value problem with upper and lower solutions in the reversed order abstract this article introduces a new concept of upper and lower solutions and studies the existence and uniqueness of solutions of second order three point boundary value problems with upper and lower solutions in the reversed order the sufficient conditions for the existence and uniqueness of solutions are obtained by using the monotone iterative method meantime the iterative sequence for solving a solution and its error estimate formula under the condition of unique solution are given some results of previous literature are extended and improved a numerical example is also included to illustrate the effectiveness of the proposed results

on the existence of positive solutions of p laplacian difference equations in this paper by means of fixed point theorem in a cone the existence of positive solutions of p laplacian difference equations is considered

existence and uniqueness results for some nonlinear boundary value problems u a s u b s0 dirichlet 2 u9 a s u9 b s 0 neumann 3 u a s u b and u9 a s u9 b periodic 4 w x here f r a r is an odd increasing homeomorphism k a b a r and w x 2 py2 f a b r a r equation 1 with f s s s s where p 1 and k t s n y 1 rt arises in the study of radial solutions for the p laplacian equation on an annular domain in n dimensions py2 n div u u q f x u u s 0 a x b x g r 5 w x and has been studied extensively see for instance 1 4 6 in this paper we shall establish existence results for 1 with each of the above boundary conditions 2 3 and 4 under various growth conditions on f in particular our results give the existence of radial solutions

fixed sign solutions of second order difference equations with neumann boundary conditions in this paper we study the existence of solution of the nonlinear second order difference problem with neumann boundary conditions assuming the existence of a pair of ordered lower and upper solutions and we obtain optimal existence results for the case and even for to this end we do an exhaustive study of the values of the real parameters and for which the associated green s function to the linear operator l u u 2 2 u 1 u with neumann boundary conditions has fixed sign

existence and uniqueness for nonlinear elliptic equations with lower order terms abstract we study the nonlinear dirichlet problem for the elliptic equation div a x u b x u div f in a regular domain r n n 2 u 0 on in hypothesis of lipschitz continuity and strong monotonicity of a we assume that the lower order term b x s verify b x s b x t e x s t for a e x and for any s t r where e is a non negative function in the lorentz space l n q n q without any control on the norm of e with f l p p 1 and q we obtain existence and uniqueness result for distributional solutions u w 1 p whenever p is close to two for q uniqueness results are obtained the main difficulty to solve the problem is due to noncoercivity of the vector field a x s a x b x s moreover no classical structure conditions are satisfied

existence and approximation of solutions for first order discontinuous difference equations with nonlinear global conditions in the presence of lower and upper solutions abstract this paper is devoted to the study of the existence of solutions of first order difference equations verifying nonlinear conditions that involve the global behavior of the solution we prove that the existence of lower and upper solutions warrants the existence of such solutions lying in the sector formed by the mentioned functions we also can prove that some classical results for differential equations are not true in general for this case

noncoercive elliptic equations with discontinuous coefficients in unbounded domains abstract in this paper we study dirichlet problems for noncoercive linear elliptic equations with discontinuous coefficients in unbounded domains exploiting a nonlinear approach we achieve existence uniqueness and regularity results

extremal solutions for the difference φ laplacian problem with nonlinear functional boundary conditions abstract in this paper we study the existence and approximation of the extremal solutions for the laplacian problem lying between a pair of a lower solution and an upper solution such that we consider general boundary functional conditions that include classical ones as separated or periodic

noncoercive nonlinear dirichlet problems in unbounded domains abstract in this paper we study noncoercive nonlinear dirichlet problems with discontinuous coefficients in unbounded domains an existence result is proved exploiting suitable coercive nonlinear approximate dirichlet problems

very weak solutions to elliptic equations with singular convection term abstract we study dirichlet problem for a nonlinear equation with a drift term despite the presence of the singular convection term we establish existence and uniqueness of a solution in spaces larger than the natural one

gradient estimates below the duality exponent we show sharp local a priori estimates and regularity results for possibly degenerate non linear elliptic problems with data not lying in the natural dual space we provide a precise non linear potential theoretic analog of classical potential theory results due to adams duke math j 42 765 778 1975 and adams and lewis studia math 74 169 182 1982 concerning morrey spaces imbedding regularity properties for this we introduce a technique allowing for a non local representation of solutions via riesz potentials in turn yielding optimal local estimates simultaneously in both rearrangement and non rearrangement invariant function spaces in fact we also derive sharp estimates in lorentz spaces covering borderline cases which remained open for some while

existence and comparison results for difference φ laplacian boundary value problems with lower and upper solutions in reverse order abstract this paper is devoted to the study of the existence and comparison results for nonlinear difference laplacian problems with mixed dirichlet neumann and periodic boundary value conditions we deduce existence of extremal solutions of periodic and neumann boundary value problems lying between a pair of lower and upper solutions given in reverse order we prove the optimality of some assumptions in