Nehari manifold approach for superlinear double phase problems with variable exponents

Ángel Crespo-Blanco; Patrick Winkert

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arXiv · 2211.09189

Nehari manifold approach for superlinear double phase problems with variable exponents

Ángel Crespo-Blanco·Patrick Winkert

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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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Ángel Crespo-Blanco, Patrick Winkert. 2022-11-16. Nehari manifold approach for superlinear double phase problems with variable exponents. https://arxiv.org/abs/2211.09189

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