An infinite dimensional Saddle Point Theorem and application
Abstract
Abstract By using the τ -topology of Kryszewski and Szulkin, we establish a natural new version of the Saddle Point Theorem for strongly indefinite functionals. The abstract result will be applied to study the existence of solutions to a strongly indefinite semilinear Schrödinger equation, where the associated functional is indefinite, that is, the functional is of the form $J(u) = \dfrac{1}{2} \langle Lu, u \rangle - \Psi (u)$ J ( u ) = 1 2 〈 L u , u 〉 − Ψ ( u ) defined on a Hilbert space X , where $L : X \to X$ L : X → X is a self-adjoint operator whose negative and positive eigenspaces are both infinite-dimensional.
Fields of Study & Subjects
Nonlinear Differential Equations Analysis
Nonlinear Partial Differential Equations
Stability and Controllability of Differential Equations
Publication details
- Journal / source
- Boundary Value Problems
- Publisher
- Springer Science and Business Media LLC
- Volume
- 2026
- Issue
- 1
- Pages
- 50–50
- Publication date
- 11 February 2026
- Language
- EN