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1. Energy solutions and concentration problem of fractional Schrödinger equation.

Author

Li, Peiluan and Yuan, Yuan

Subjects
SCHRODINGER equation, PARTIAL differential equations, PERTURBATION theory, APPROXIMATION theory, MATHEMATICS
Abstract

In this paper, we consider a fractional Schrödinger equation with steep potential well and sublinear perturbation. By virtue of variational methods, the existence criteria of infinitely many nontrivial high or small energy solutions are established. In addition, the phenomenon of the concentration of solutions is also explored. We also give some examples to demonstrate the main results. [ABSTRACT FROM AUTHOR]

Published
2018
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2. A Schrödinger singular perturbation problem

Author

Ramm, A.G.

Subjects
*EQUATIONS, *SCHRODINGER equation, *PERTURBATION theory, *APPROXIMATION theory, *MATHEMATICS
Abstract

Abstract: Consider the equation −ε 2 Δu ε + q(x)u ε = f(u ε ) in , ∣u(∞)∣<∞, ε =const>0. Under what assumptions on q(x) and f(u) can one prove that the solution u ε exists and lim ε→0 u ε = u(x), where u(x) solves the limiting problem q(x)u = f(u)? These are the questions discussed in the paper. [Copyright &y& Elsevier]

Published
2007
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