Two nonlinear days in Urbino 2017. Electron. J. Diff. Eqns., Conference 25 (2018), pp. 213-219.

Kirchhoff-type problems involving nonlinearities satisfying only subcritical and superlinear conditions

Biagio Ricceri

Abstract:
In this note, we study the problem
$$\displaylines{ -h\Big(\int_{\Omega}|\nabla u(x)|^2dx\Big)\Delta u=f(u) \quad \text{in } \Omega\cr u\big|_{\partial\Omega}=0. }$$
As an application of a general multiplicity result, we establish the existence of at least three solutions, two of which are global minimizers 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 required.

Published September 15, 2018.
Math Subject Classifications: 35J20, 35J61, 49K40, 90C26.
Key Words: Kirchhoff-type problems; multiplicity of global minimizers; variational methods.

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Biagio Ricceri
Department of Mathematics
University of Catania
Viale A. Doria, 95125 Catania, Italy
email: ricceri@dmi.unict.it

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