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Existence of positive solutions for nonlinear Dirichlet problems with gradient dependence and arbitrary growth

Nikolaos S. PapageorgiouCalogero VetroFrancesca Vetro

subject

pseudomonotone mapApplied Mathematicsnonlinear maximum principle010102 general mathematicsconvection reaction term01 natural sciencesDirichlet distribution010101 applied mathematicshartman conditionNonlinear systemsymbols.namesakeSettore MAT/05 - Analisi Matematicapicone identitysymbolsQA1-939Applied mathematicsnonlinear regularity0101 mathematicsMathematicsMathematics

description

We consider a nonlinear elliptic problem driven by the Dirichlet $p$-Laplacian and a reaction term which depends also on the gradient (convection). No growth condition is imposed on the reaction term $f(z, \cdot,y)$. Using topological tools and the asymptotic analysis of a family of perturbed problems, we prove the existence of a positive smooth solution.

yearjournalcountryeditionlanguage
2018-04-01Electronic Journal of Qualitative Theory of Differential Equations
10.14232/ejqtde.2018.1.18http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1&paramtipus_ertek=publication&param_ertek=6310