For a class of quasilinear elliptic equations involving the p-Laplace operator, we develop an abstract critical point theory in the presence of sub-supersoIutions. Our approach is based upon the proof of the invariance under the gradient flow of enlarged cones in the Wg(0)(1,P) 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
Boureanu, M., Noris, B., Terracini, S. (2013). Sub and supersolutions, invariant cones and multiplicity results for p-Laplace equations. In J.B. Serrin, E.L. Mitidieri, V.D. Rădulescu (a cura di), Recent Trends in Nonlinear Partial Differential Equations II: Stationary Problems (pp. 91-119). American Mathematical Society [10.1090/conm/595/11800].
Sub and supersolutions, invariant cones and multiplicity results for p-Laplace equations
NORIS, BENEDETTA;
2013
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-supersoIutions. Our approach is based upon the proof of the invariance under the gradient flow of enlarged cones in the Wg(0)(1,P) 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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