Nehari manifold approach for superlinear double phase problems with variable exponents

2023/12/15 by Crespo-Blanco, Ángel, Winkert, Patrick
#500 Naturwissenschaften und Mathematik::510 Mathematik::510 Mathematik #Nehari manifold #double phase operator with variable exponent #existence of solutions #mountain pass theorem #multiple solutions

paper · doi:10.14279/depositonce-19679

Abstract

In this paper we consider quasilinear elliptic equations driven by the variable exponent double phase operator with superlinear right-hand sides. Under very general assumptions on the nonlinearity, we prove a multiplicity result for such problems whereby we show the existence of a positive solution, a negative one and a solution with changing sign. The sign-changing solution is obtained via the Nehari manifold approach and, in addition, we can also give information on its nodal domains.

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