In this paper we prove an existence theorem for positive solutions of a nonlinear Dirichlet problem involving the $p$-Laplacian operator on a smooth bounded domain when a nonlinearity depending on the gradient is considered. Our main theorem extends a previous result by Ruiz in J. Diff. Equations 2004, in which a slight modification of the celebrated blowup technique due to Gidas and Spruck in 1981 is developed.
Existence of solutions for quasilinear Dirichlet problems with gradient terms
Filippucci, Roberta;
2019
Abstract
In this paper we prove an existence theorem for positive solutions of a nonlinear Dirichlet problem involving the $p$-Laplacian operator on a smooth bounded domain when a nonlinearity depending on the gradient is considered. Our main theorem extends a previous result by Ruiz in J. Diff. Equations 2004, in which a slight modification of the celebrated blowup technique due to Gidas and Spruck in 1981 is developed.File in questo prodotto:
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