Existence and multiplicity of solutions to equations of N−N-Laplacian type with critical exponential growth in RN\mathbb{R}^{N}

In this paper, we deal with the existence and multiplicity of solutions to the nonuniformly elliptic equation of the N-Lapalcian type with a potential and a nonlinear term of critical exponential growth and satisfying the Ambrosetti-Rabinowitz condition. In spite of a possible failure of the Palais-Smale compactness condition, in this article we apply minimax method to obtain the weak solution to such an equation. In particular, in the case of $N-$Laplacian, using the minimization and the Ekeland variational principle, we obtain multiplicity of weak solutions. Finally, we will prove the above results when our nonlinearity doesn't satisfy the well-known Ambrosetti-Rabinowitz condition and thus derive the existence and multiplicity of solutions for a much wider class of nonlinear terms $f$.Comment: 30 pages. First draft in November, 201

Community service: it always means more when it comes from the heart

Community service itself is a voluntary activity. It is up to students to choose and it should not be an obligation or an assignment. Students need to have an opinion on what they want to do as service so that they will enjoy the experience and thus be able to learn from it