Quasilinear elliptic equations involving the \(N\)-Laplacian with critical exponential growth in \(\mathbb R^N\). (English) Zbl 1180.35262

Summary: This paper shows the existence of nontrivial solutions for the quasilinear equations of the form \[ -\Delta_N u+V(x)|u|^{N-2}u-\Delta_N(u^2)u= h(u)\quad \text{in }\mathbb R^N, \]
where \(\Delta_N\) is the \(N\)-Laplacian operator, \(V\) is a continuous function bounded from below away from zero and \(h(u)\) is a continuous function having critical exponential growth.


35J92 Quasilinear elliptic equations with \(p\)-Laplacian
35J20 Variational methods for second-order elliptic equations
35B33 Critical exponents in context of PDEs
Full Text: DOI


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