The fibering method approach for a non-linear Schrödinger equation coupled with the electromagnetic field
Kaye Silva
2020LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Científicas)49 citationsDOIOpen Access PDF
Abstract
We study, with respect to the parameter q 6 ≠ 0, the following Schrödinger- Bopp-Podolsky system in R3{equation presented} where p ε (2; 3], ω > 0, a ≥ 0 are fixed. We prove, by means of the fibering approach, that the system has no solutions at all for large values of q and has two radial solutions for small q's. We give also qualitative properties about the energy level of the solutions and a variational characterization of these extremal values of q. Our results recover and improve some results in [2, 5].
Topics & Concepts
MathematicsElectromagnetic fieldField (mathematics)Mathematical analysisMathematical physicsApplied mathematicsPure mathematicsPhysicsQuantum mechanicsNonlinear Partial Differential EquationsAdvanced Mathematical Physics ProblemsAdvanced Mathematical Modeling in Engineering