Superlinear elliptic equations with unbalanced growth and nonlinear boundary condition

2025/04/28 by Amoroso, Eleonora, Crespo-Blanco, Ángel, Pucci, Patrizia +1
#500 Naturwissenschaften und Mathematik::510 Mathematik::510 Mathematik #Brouwer degree #Nehari manifold #double phase operator #nonlinear boundary condition #nonstandard growth #sign-changing solution

paper · doi:10.14279/depositonce-23547

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 boundary condition 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.

Related

• Superlinear elliptic equations with unbalanced growth and nonlinear boundary condition
• Parametric superlinear double phase problems with singular term and critical growth on the boundary
• Nehari manifold approach for superlinear double phase problems with variable exponents
• Nehari manifold approach for superlinear double phase problems with variable exponents
• Sign changing solution for a double phase problem with nonlinear boundary condition via the Nehari manifold