Work

Superlinear elliptic equations with unbalanced growth and nonlinear boundary condition

Year: 2024

Type: article

Abstract: In this paper we first introduce an innovative equivalent norm in the Musielak-Orlicz Sobolev spaces in a very general setting and we then present a new result on the boundedness of the solutions of a wide class of nonlinear Neumann problems, both of independent interest. Moreover, we study a variable exponent double phase problem with a nonlinear boundarycondition and prove the existence of multiple solutions under very general assumptions on the nonlinearities. To be more precise, we get constant sign solutions (nonpositive and nonnegative) via a mountain-pass approach and a sign- changing solution by using an appropriate subset of the corresponding Nehari manifold along with the Brouwer degree and the Quantitative Deformation Lemma.

Source: Bulletin des Sciences Mathématiques

DOI: 10.1016/j.bulsci.2024.103534

Authors: Eleonora Amoroso, Ángel Crespo-Blanco, Patrizia Pucci, Patrick Winkert

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,200