Work

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

Year: 2025

Type: article

Abstract: We present an abstract critical point theorem about the existence of infinitely many critical orbits to strongly indefinite functionals with a sign-changing nonlinear part defined on a dislocation space with a discrete group action. We apply the abstract result to a Schrödinger equation $$\begin{aligned} -\Delta u + V(x) u = f(u) - \lambda g(u) \end{aligned}$$ - Δ u + V ( x ) u = f ( u ) - λ g ( u ) with 0 in the spectral gap of the Schrödinger operator $$-\Delta + V(x)$$ - Δ + V ( x ) , that appears in nonlinear optics. We also consider equations with singular potentials arising from the study of cylindrically symmetric, electromagnetic waves to the system of Maxwell equations.

Source: Calculus of Variations and Partial Differential Equations

DOI: 10.1007/s00526-025-03112-4

Authors: Federico Bernini, Bartosz Bieganowski, Daniel Strzelecki

Institutions: University of Milano-Bicocca, University of Warsaw

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190