Nodal and multiple constant sign solutions for resonant p-Laplacian equations with a nonsmooth potential

By Leszek Gasinski, Nikolaos S. Papageorgiou. 2009

52 citations recorded by the source corpus.

Abstract In this paper we study a nonlinear Dirichlet elliptic differential equation driven by the p -Laplacian and with a nonsmooth potential (hemivariational inequality). Using a variational approach combined with suitable truncation techniques and the method of upper–lower solutions, we prove the existence of five nontrivial smooth solutions, two positive, two negative and the fifth nodal. Our hypotheses on the nonsmooth potential allow resonance at infinity with respect to the principal eigenvalue λ 1 > 0 of ( − Δ p , W 0 1 , p ( Z ) ) .

Subfields: Applied Mathematics, Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/08d7a3ffc88ddfa00c58a469f947f19fe6a3a469

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In Applied Mathematics

In Computational Theory and Mathematics

In Numerical Analysis

Citations in the corpus

On a Class of Parametric (p, 2)-equations (2016, background): “The second deformation theorem (see, for example, Gasinski and Papageorgiou [16, p. 628]), implies that this definition is independent of the choice of the level c < inf ϕ(Kϕ).”
Multiple Solutions for Nonlinear Coercive Problems with a Nonhomogeneous Differential Operator and a Nonsmooth Potential (2012, background): “(4.20) (see Aizicovici-Papageorgiou-Staicu [1, proof of Proposition 29] or GasińskiPapageorgiou [20, Theorem 3.4]).”
Anisotropic nonlinear Neumann problems (2011, unknown): “We mention the works of Bartsch–Liu [6], Carl–Perera [8], Dancer–Perera [12], Filippakis–Kristaly– Papageorgiou [20], Gasiński–Papageorgiou [23], Liu–Liu [30], Papageorgiou–Papageorgiou [34,35] and Zhang–Chen–Li [38].”