Existence results for a Dirichlet boundary value problem through a local minimization principle

Year 2023, Volume: 52 Issue: 1, 126 - 135, 15.02.2023

Armin Hadjian , Juan Nieto

https://doi.org/10.15672/hujms.988476

Abstract

In this paper, a local minimum result for differentiable functionals is exploited in order to prove that a perturbed Dirichlet boundary value problem including a Lipschitz continuous non-linear term admits at least one non-trivial weak solution under an asymptotical behaviour of the nonlinear datum at zero. Some special cases and a concrete example of an application is then presented.

Keywords

Dirichlet boundary value problem, variational methods, existence results

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