An abstract linking theorem applied to indefinite problems via spectral\n properties

2018/07/29 by Liliane A. Maia, Maia, Liliane A., Mayra Veloso Ayrimoraes Soares +1
Computer Science · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Matrix Theory and Algorithms #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1807.11155

openalex publication_date 2018/07/29 · openalex created_date 2022/08/04 · openalex updated_date 2026/07/28

Abstract

An abstract linking result for Cerami sequences is proved without the Cerami\ncondition. It is applied directly in order to prove the existence of critical\npoints for a class of indefinite problems in infinite dimensional Hilbert\nSpaces. The main applications are given to Hamiltonian systems and Schrodinger\nequations. Here spectral properties of the operators are exploited and\nhypotheses of monotonicity on the nonlinearities are discarded.\n

Related

• A new infinite-dimensional Linking theorem with application to a system of coupled Poisson equations
• An infinite dimensional saddle point theorem and application
• Spectral Theory Approach for a Class of Radial Indefinite Variational Problems
• Multiplicity of critical orbits to nonlinear, strongly indefinite functionals with sign-changing nonlinear part
• Nontrivial solutions for periodic Schrödinger equations with sign-changing nonlinearities