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

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

References

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