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arXiv · 1808.06204

Spectral Theory Approach for a Class of Radial Indefinite Variational Problems

Mayra Soares·Liliane Maia
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Abstract

Considering the radial nonlinear Schrodinger equation - \Delta u + V(x)u = g(x,u) in R^N, N \geq 3 we aim to find a radial nontrivial solution for it, where V changes sign ensuring this problem is indefinite and g is an asymptotically linear nonlinearity. We work with variational methods associating to the problem an indefinite functional in order to apply our Abstract Linking Theorem for Cerami sequences in [8] to get a non-trivial critical point for this functional. Our goal is to make use of spectral properties of operator A:= - \Delta + V(x) restricted to H^1_{rad}(R^N), the space of radially symmetric functions in H^1(R^N), for obtaining a linking geometry structure to the problem and by means of special properties of radially symmetric functions get the necessary compactness.

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Mayra Soares, Liliane Maia. 2018-08-19. Spectral Theory Approach for a Class of Radial Indefinite Variational Problems. https://arxiv.org/abs/1808.06204

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