2019/04/30 by Mayra Soares, Mayra Veloso Ayrimoraes Soares, Soares, Mayra +2 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Applied mathematics #Cellular Automata and Applications #Compact space #Computability, Logic, AI Algorithms #FOS: Mathematics #Infinity #Limit (mathematics) #Limit point #Mathematical analysis #Mathematics #Monotonic function #Nonlinear Partial Differential Equations #Nonlinear system #Numerical methods in inverse problems #Operator (biology) #Physics #Pure mathematics #Quantum mechanics #Scheduling and Optimization Algorithms #Spectrum (functional analysis) #Zero (linguistics) #math.AP
paper · pdf · doi:10.48550/arxiv.1905.00121
published in arXiv (Cornell University) (Cornell University) · 22
openalex publication_date 2019/04/30 · arxiv created 2019/09/19 · arxiv updated 2019/09/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
We present a new approach to solve a Schrödinger Equation autonomous at infinity, by identifying the relation between the arrangement of the spectrum of the concerned operator and the behavior of the nonlinearity at zero and at infinity. In order to apply variational methods, we set up a suitable linking structure depending on the growth of the nonlinear term and making use of information about the autonomous problem at infinity. Our method allows us to circumvent the lack of compactness. The main novelty is that none monotonicity assumption is required on the nonlinearity, which may be sign-changing as well as the potential. Furthermore, depending on the nonlinearity, the limit of the potential at infinity may be non-positive, so that zero may be an interior point in the essential spectrum of the Schrödinger operator.