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arXiv · 1805.01909

Systems of coupled Schr\"odinger equations with sign-changing nonlinearities via classical Nehari manifold approach

Bartosz Bieganowski
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Abstract

We propose existence and multiplicity results for the system of Schr\"odinger equations with sign-changing nonlinearities in bounded domains or in the whole space $\mathbb{R}^N$. In the bounded domain we utilize the classical approach via the Nehari manifold, which is (under our assumptions) a differentiable manifold of class $\mathcal{C}^1$ and the Fountain theorem by Bartsch. In the space $\mathbb{R}^N$ we additionally need to assume the $\mathbb{Z}^N$-periodicity of potentials and our proofs are based on the concentration-compactness lemma by Lions and the Lusternik-Schnirelmann values.

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Bartosz Bieganowski. 2018-05-04. Systems of coupled Schr\"odinger equations with sign-changing nonlinearities via classical Nehari manifold approach. https://doi.org/10.1080/17476933.2018.1514029

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