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arXiv · 1210.2274

Sub and supersolutions, invariant cones and multiplicity results for p-Laplace equations

Maria-Magdalena Boureanu·Benedetta Noris·Susanna Terracini
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Abstract

For a class of quasilinear elliptic equations involving the p-Laplace operator, we develop an abstract critical point theory in the presence of sub-supersolutions. Our approach is based upon the proof of the invariance under the gradient flow of enlarged cones in the $W^{1,p}_0$ topology. With this, we prove abstract existence and multiplicity theorems in the presence of variously ordered pairs of sub-supersolutions. As an application, we provide a four solutions theorem, one of the solutions being sign-changing.

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Maria-Magdalena Boureanu, Benedetta Noris, Susanna Terracini. 2012-10-08. Sub and supersolutions, invariant cones and multiplicity results for p-Laplace equations. https://arxiv.org/abs/1210.2274

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