Existence of a priori bounded solutions for discrete two-point boundary value problems

In this paper, we investigate positive solutions of boundary value problems for a general second-order nonlinear difference equation, which includes a Jacobi operator and a parameter λ. Based on the critical point theory, we obtain the existence of three solutions for the boundary value problem. Then, we establish a strong maximum principle for this problem and obtain some determined open intervals of the parameter λ for the existence of at least two positive solutions. In the end, we give two examples to illustrate our main results.

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Existence and approximation of a solution for a two point nonlinear Dirichlet problem

Candito,

Livrea,

Sanchez

2024

DCDS-S

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Existence of a priori bounded solutions for discrete two-point boundary value problems

Cited by 3 publications

References 19 publications

Existence of positive solutions for second-order differential equations with two-point boundary value problems involving p-Laplacian

Existence of positive solutions for second-order differential equations with two-point boundary value problems involving p-Laplacian

Positive Solutions of Boundary Value Problems for General Second-Order Nonlinear Difference Equations

Existence and approximation of a solution for a two point nonlinear Dirichlet problem

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