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asymptotically periodic problems

Proceedings of the Royal Society of Edinburgh Section A: Mathematics (1)

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1 results

Schrödinger equations with asymptotically periodic terms
Part of
- Elliptic equations and systems
Reinaldo de Marchi
Journal:

Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 145 / Issue 4 / August 2015

Published online by Cambridge University Press:

30 June 2015, pp. 745-757

Print publication:

August 2015
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We study the existence of non-trivial solutions for a class of asymptotically periodic semilinear Schrödinger equations in ℝN. By combining variational methods and the concentration-compactness principle, we obtain a non-trivial solution for the asymptotically periodic case and a ground state solution for the periodic one. In the proofs we apply the mountain pass theorem and its local version.