Semilinear elliptic equations with dependence on the gradient via mountain-pass techniques

By D. G. Figueiredo, M. Girardi, M. Matzeu. Differential and Integral Equations, 2004

139 citations recorded by the source corpus.

A class of semilinear elliptic equations with dependence on the gradient is considered. The existence of a positive and a negative solution is stated through an iterative method based on Mountain Pass techniques

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/d318d314c4fc0551f73c1b9d8e0ac5f10be01e0f

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

Existence and uniqueness results for double phase problems with convection term (2019, methodology): “For other existence results on quasilinear equations with convection term and the p-Laplace or the (p, q)-Laplace differential operator we refer to the papers of Bai-Gasiński-Papageorgiou [6], De Figueiredo-Girardi-Matzeu [12], Dupaigne-Ghergu-Rădulescu [13], Faraci-MotreanuPuglisi [14], Faria-Miyag”
Positive solutions for nonlinear Neumann problems with singular terms and convection (2020, background): “rms have been investigated separately, primarily in the context of Dirichlet problems. For singular problems, we mention the works of Giacomoni, Schindler & Takac [7], Hirano, Saccon & Shioji [1], Papageorgiou & Ra˘dulescu [16], Papageorgiou, Ra˘dulescu & Repovˇs [19, 21], Papageorgi”
Positive solutions of quasi-linear elliptic equations with dependence on the gradient (2015, methodology): “A different approach is proposed in [7] where the authors prove the existence of a positive and a negative solution for (P ), when p = 2, through an iterative method involving Mountain Pass technique assuming that f(x, s, ξ) satisfies Lipschitz conditions on s and ξ in a neighborhood of zero and has”