Nontrivial complex solutions for magnetic Schrodinger equations with critical nonlinearities
Date
2018-10-22
Authors
Barile, Sara
Figueiredo, Giovany M.
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
Using minimization arguments we establish the existence of a complex solution to the magnetic Schrödinger equation
-(∇ + iA(x))2u + u = ƒ(|u|2)u in ℝN,
where N ≥ 3, A:ℝN → ℝN is the magnetic potential and ƒ satisfies some critical growth assumptions. First we obtain bounds from a real Pohozaev manifold. Then relate them to Sobolev imbedding constants and to the least energy level associated with the real equation in absence of the magnetic field (i.e., with A(x) = 0). We also apply the Lions Concentration Compactness Principle to the modula of the minimizing sequences involved.
Description
Keywords
Magnetic Schrödinger equations, Critical nonlinearities, Minimization problem, Concentration-compactness methods, Pohozaev manifold
Citation
Barile, S., & Figueiredo, G. M. (2018). Nontrivial complex solutions for magnetic Schrodinger equations with critical nonlinearities. <i>Electronic Journal of Differential Equations, 2018</i>(174), pp. 1-21.
Rights
Attribution 4.0 International