A multiplicity theorem for problems with the p-Laplacian

By Dumitru Motreanu, Viorica V. Motreanu, Nikolaos S. Papageorgiou. 2007

71 citations recorded by the source corpus.

Abstract We consider nonlinear elliptic equations driven by the p -Laplacian differential operator. Using degree theoretic arguments based on the degree map for operators of type ( S ) + , we prove the existence of two nontrivial smooth solutions, one of which is of constant sign.

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

View Paper: https://www.semanticscholar.org/paper/6f368fc731314818b37b8ea39641ae945379faea

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In Applied Mathematics

In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

Multiple Solutions for Nonlinear Coercive Problems with a Nonhomogeneous Differential Operator and a Nonsmooth Potential (2012, methodology): “We mention that three solutions theorems for coercive equations were proved by Ambrosetti-Lupo [2], Ambrosetti-Mancini [3], Iannizzotto [24], Struwe [34] for certain parametric semilinear equations (Iannizzotto [24] deals with hemivariational inequalities, while the other consider “smooth” problems)”
Multiple constant sign and nodal solutions for nonlinear elliptic equations with the p-Laplacian (2008, unknown): “Then as in Motreanu, Motreanu and Papageorgiou [21], we can find ρ > 0 small such that φλ+(x0) < inf [ φλ+(x): ‖x − x0‖ = ρ ] = cρ.”
Infinitely many solutions for p-Laplacian equation involving critical Sobolev growth (2012, background): “The readers can refer to [10,11,13,14,16,23] for some recent results for quasilinear elliptic problems with critical nonlinearities.”
Multiple solutions with precise sign for nonlinear parametric Robin problems (2014, background): “Extensions to Dirichlet p-Laplacian equations can be found in Papageorgiou and Papageorgiou [18].”
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].”