Existence of positive solutions to anisotropic elliptic equations in the entire Euclidean space

Rulong Xie; Hailian Wang; Lei Yang

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arXiv · 2610.17601

Existence of positive solutions to anisotropic elliptic equations in the entire Euclidean space

Rulong Xie·Hailian Wang·Lei Yang

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Abstract

In this paper, we research an anisotropic elliptic equation in the entire Euclidean space R^{N} . Under the assumption that the nonlinearity of the equation has exponential or critical growth, we prove, by means of the mountain-pass theorem, that the equation admits a nontrivial positive weak solution. Moreover, applying the mountain-pass theorem and Ekeland's variational principle, we show that a perturbation of the equation possesses two distinct positive weak solutions.

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BibTeX RIS

Rulong Xie, Hailian Wang, Lei Yang. 2026-10-13. Existence of positive solutions to anisotropic elliptic equations in the entire Euclidean space. https://arxiv.org/abs/2610.17601

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