Work

Existence of Solutions to Nonlinear 2nth-order Discrete Boundary Value Problem with Parameter Dependence

Year: 2025

Type: article

Abstract: This paper presents several sufficient conditions for the existence of at least one solution and at least one nonzero solution to the boundary value problem $$\begin{aligned} \Delta ^{n} (p(k) \Delta ^{n}x(k-n)) = \lambda f(k, x(k)), & k \in {\mathbb N}[n,T] \\ x(0)=x(1)=\ldots =x(n-1) =0, & \\ x(T+1)=x(T+2)= \ldots = x(T+n)=0, & \end{aligned}$$ with a parameter $$\lambda $$ . The technical approach is based on variational methods and the Mountain pass lemma.

Source: Results in Mathematics

DOI: 10.1007/s00025-025-02444-z

Authors: Urszula Ostaszewska, Ewa Schmeidel, Malgorzata Zdanowicz

Institution: University of Białystok

Language: English

Topic: Nonlinear Differential Equations Analysis

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

OpenAlex ID: W4411262846