EXISTENCE OF SOLUTIONS OF nTH-ORDER NONLINEAR DIFFERENCE EQUATIONS WITH GENERAL BOUNDARY CONDITIONS

doi:10.1007/s10473-020-0115-y

Abstract

Abstract: The aim of this paper is to prove the existence of one or multiple solutions of nonlinear difference equations coupled to a general set of boundary conditions. Before to do this, we construct a discrete operator whose fixed points coincide with the solutions of the problem we are looking for. Moreover, we introduce a strong positiveness condition on the related Green's function that allows us to construct suitable cones where to apply adequate fixed point theorems. Once we have the general existence result, we deduce, as a particular case, the existence of solutions of a second order difference equation with nonlocal perturbed Dirichlet conditions.

Key words: difference equation, multiplicity of solutions, Green's function, positive solutions, parameter dependence

CLC Number:

39A10

Alberto CABADA, Nikolay DIMITROV. EXISTENCE OF SOLUTIONS OF nTH-ORDER NONLINEAR DIFFERENCE EQUATIONS WITH GENERAL BOUNDARY CONDITIONS[J].Acta mathematica scientia,Series B, 2020, 40(1): 226-236.

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