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arXiv · 1710.05676

Kirchhoff-type problems involving subcritical and superlinear nonlinearities satisfying no further condition

Biagio Ricceri
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Abstract

In this note, we deal with a problem of the type $$\cases {-h\left ( \int_{\Omega}|\nabla u(x)|^2dx\right ) \Delta u=f(u) & in $\Omega$\cr & \cr u_{|\partial\Omega}=0\ .\cr}$$ As an application of a new general multiplicity result, we establish the existence of at least three solutions, two of which are global minima of the related energy functional. The only condition assumed on $f$ is that it be subcritical and superlinear: no condition on the behaviour of $f$ at $0$ is requested.

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Biagio Ricceri. 2017-10-16. Kirchhoff-type problems involving subcritical and superlinear nonlinearities satisfying no further condition. https://arxiv.org/abs/1710.05676

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