Generalized linking-type theorem with applications to strongly indefinite problems with sign-changing nonlinearities

We show a linking-type result which allows us to study strongly indefinite problems with sign-changing nonlinearities. We apply the abstract theory to the singular Schrödinger equation - Δ u + V ( x ) u + a r 2 u = f ( u ) - λ g ( u ) , x = ( y , z ) ∈ R K × R N - K , r = | y | , where 0 ∉ σ - Δ + a...

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Published in:Calculus of variations and partial differential equations 2022-10, Vol.61 (5), Article 182
Main Authors: Bernini, Federico, Bieganowski, Bartosz
Format: Article
Language:English
Subjects:
Analysis
Calculus of Variations and Optimal Control
Optimization
Control
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Nonlinearity
Schrodinger equation
Systems Theory
Theoretical
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description We show a linking-type result which allows us to study strongly indefinite problems with sign-changing nonlinearities. We apply the abstract theory to the singular Schrödinger equation - Δ u + V ( x ) u + a r 2 u = f ( u ) - λ g ( u ) , x = ( y , z ) ∈ R K × R N - K , r = | y | , where 0 ∉ σ - Δ + a r 2 + V ( x ) . As a consequence we obtain also the existence of solutions to the nonlinear curl-curl problem.
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subjects Analysis
Calculus of Variations and Optimal Control
Optimization
Control
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Nonlinearity
Schrodinger equation
Systems Theory
Theoretical
title Generalized linking-type theorem with applications to strongly indefinite problems with sign-changing nonlinearities
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