Sign-changing and multiple solutions for the $p$-Laplacian

By Siegfried Carl, Kanishka Perera. 2002

86 citations recorded by the source corpus.

We obtain a positive solution, a negative solution, and a sign-changing solution for a class of p-Laplacian problems with jumping nonlinearities using variational and super-subsolution methods.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/5d85aa4adeef724b6a2a0a6f55d429518c5cdeb6

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

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].”
Multiple constant sign and nodal solutions for nonlinear elliptic equations with the p-Laplacian (2008, methodology): “We have the works of Bartsch and Liu [4], Carl and Perera [6], Zhang and Li [25] and Zhang, Chen and Li [24].”
Existence of five nonzero solutions with exact sign for A p-laplacian equation (2009, methodology): “Recently, Carl-Motreanu [9] and Carl-Perera [10] extended the work of Dancer-Du [19] to a nonsmooth setting which involves the p-Laplacian.”
Existence of multiple solutions with precise sign information for superlinear Neumann problems (2009, background): “[25], Papageorgiou and Papageorgiou [27] for p-superlinear Dirichlet problems and by Carl and Perera [10], Zhang and Li [32], Zhang et al.”