Critical point approaches to nonlinear square root Laplacian equations

Bohner, Martin and Caristi, Giuseppe and Heidarkhani, Shapour and Salari, Amjad (2024) Critical point approaches to nonlinear square root Laplacian equations. Miskolc Mathematical Notes, 25 (1). pp. 153-164. ISSN 1787-2413

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Abstract

This work is devoted to the study of multiplicity results of solutions for a class of nonlinear equations involving the square root of the Laplacian. Indeed, we will use variational methods for smooth functionals, defined on reflexive Banach spaces, in order to achieve the existence of at least three solutions for the equations. Moreover, assuming that the nonlinear terms are nonnegative, we will prove that the solutions are nonnegative. Finally, by presenting an example, we will ensure the applicability of our results.

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