Existence, nonexistence, and asymptotic behavior of solutions for N-Laplacian equations involving critical exponential growth in the whole ℝ^N

2020/09/08 by Anderson L. A. de Araújo, de Araujo, Anderson L. A., Luiz F. O. Faria +1
Mathematics · Computer Science · #Nonlinear Partial Differential Equations #Advanced Mathematical Modeling in Engineering #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.2009.03845

Abstract

In this paper, we are interested in studying the existence or non-existence of solutions for a class of elliptic problems involving the N-Laplacian operator in the whole space. The nonlinearity considered involves critical Trudinger-Moser growth. Our approach is non-variational, and in this way, we can address a wide range of problems not yet contained in the literature. Even W^1,N(ℝ^N)\hookrightarrow L^∞(ℝ^N) failing, we establish ‖u_λ‖_L^∞(ℝ^N) ≤ C ‖u‖_W^1,N(ℝ^N)^Θ (for some Θ>0), when u is a solution. To conclude, we explore some asymptotic properties.

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