Positive solutions of quasilinear elliptic equations with exponential nonlinearity combined with convection term

2018/08/27 by de Araujo, Anderson Luis Albuquerque, Faria, Luiz Fernando de Oliveira
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1808.08805

Abstract

We establish the existence of positive solutions for a nonlinear elliptic Dirichlet problem in dimension N involving the N-Laplacian. The nonlinearity considered depends on the gradient of the unknown function and an exponential term. In such case, variational methods cannot be applied. Our approach is based on approximation scheme, where we consider a new class of normed spaces of finite dimension. As a particular case, we extended the result achieved by De Araujo and Montenegro [2016] for any N>2.

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