Multiple constant sign and nodal solutions for nonlinear elliptic equations with the p-Laplacian

By Michael E. Filippakis, Nikolaos S. Papageorgiou. 2008

94 citations recorded by the source corpus.

We consider a nonlinear elliptic equation driven by the p-Laplacian with Dirichlet boundary conditions. Using variational techniques combined with the method of upper–lower solutions and suitable truncation arguments, we establish the existence of at least five nontrivial solutions. Two positive, two negative and a nodal (sign-changing) solution. Our framework of analysis incorporates both coercive and p-superlinear problems. Also the result on multiple constant sign solutions incorporates the case of concave–convex nonlinearities.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/926be4eeb7033876391cadd9dc4021a7faef7798

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In Applied Mathematics

In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

Positive solutions for perturbations of the Robin eigenvalue problem plus an indefinite potential (2017, background): “We again have that S(λ) is downward directed (that is, if u1, u2 ∈ S(λ), then we can find u ∈ S(λ) such that u ≤ u1, u ≤ u2; see Filippakis & Papageorgiou [5]).”
Nonlinear nonhomogeneous singular problems (2019, background): “1 of Filippakis & Papageorgiou [9], where a similar result is proved for the upper solutions of nonlinear Dirichlet problems without singularities, driven by the p-Laplacian (see also Papageorgiou, Rădulescu & Repovš [33, 34], for Robin problems).”