Nonlinear Schrödinger equations via fixed point principles


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.


Mihaela Manole

Radu Precup
Department of Mathematics, Babes-Bolyai University, Cluj-Napoca, Romania


Nonlinear Schrodinger equation; weak solution; nonlinear operator; fixed point.

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M. Manole, R. Precup, Nonlinear Schrodinger equations via fixed point principles, Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal. 18 (2011), 705-718.


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Dynamics of Continuous, Discrete & Impulsive Systems

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