Abstract
This paper deals with weak solvability of the Cauchy-Dirichlet problem for the perturbed time-dependent Schrödinger equation. We use the operator approach based on fixed point theorems and properties of norm estimation and compactness of the solution operator associated to the nonhomogeneous linear Schrödinger equation. Also applied previously by the second author to nonlinear heat and wave equations, our operator method provides a unified way for treating different types of nonlinear boundary value problems.
Authors
Mihaela Manole
Radu Precup
Department of Mathematics, Babes-Bolyai University, Cluj-Napoca, Romania
Keywords
Nonlinear Schrodinger equation; weak solution; nonlinear operator; fixed point.
Paper coordinates
M. Manole, R. Precup, Nonlinear Schrodinger equations via fixed point principles, Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal. 18 (2011), 705-718.
About this paper
Journal
Dynamics of Continuous, Discrete & Impulsive Systems
Publisher Name
–
paper on journal website
Print ISSN
1201-3390
Online ISSN
1918-2538
google scholar link
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