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arXiv · 2410.13315

Multiplicity of critical orbits to nonlinear, strongly indefinite functionals with sign-changing nonlinear part

Federico Bernini·Bartosz Bieganowski·Daniel Strzelecki
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Abstract

We show an abstract critical point theorem about existence of infinitely many critical orbits to strongly indefinite functionals with sign-changing nonlinear part defined on a dislocation space with a discrete group action. We apply the abstract result to a Schr\"odinger equation $$ -\Delta u + V(x) u = f(u) - \lambda g(u) $$ with $0$ in the spectral gap of the Schr\"odinger operator $-\Delta + V(x)$, that appears in nonlinear optics, as well as to the equations with singular potentials arising from the study of cylindrically symmetric, electromagnetic waves to the system of Maxwell equations.

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Federico Bernini, Bartosz Bieganowski, Daniel Strzelecki. 2024-10-17. Multiplicity of critical orbits to nonlinear, strongly indefinite functionals with sign-changing nonlinear part. https://arxiv.org/abs/2410.13315

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