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arXiv · 2505.12936

Elliptic Problems Involving Mixed Local-Nonlocal Operator in the Hyperbolic Space

Diksha Gupta·Konijeti Sreenadh
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Abstract

This paper explores the existence of solutions to a class of nonlinear elliptic equations involving a mixed local-nonlocal operator of the form $-\Delta_{\mathbb{B}^N} + (-\Delta_{\mathbb{B}^N})^s$, with $0 < s < 1$, set in the hyperbolic space $\mathbb{B}^N$. By employing variational methods, we address both subcritical and critical nonlinearities, establishing the existence of weak solutions under appropriate conditions.

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Diksha Gupta, Konijeti Sreenadh. 2025-05-19. Elliptic Problems Involving Mixed Local-Nonlocal Operator in the Hyperbolic Space. https://arxiv.org/abs/2505.12936

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