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arXiv · 2606.29348

Mixed local-nonlocal quasilinear problems with mixed interpolated Hardy potential

Yergen Aikyn·Sekhar Ghosh·Vishvesh Kumar·Michael Ruzhansky
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Abstract

This paper addresses the existence of nontrivial solutions to a class of mixed local-nonlocal problems involving a mixed interpolated Hardy potential. We first establish a concentration-compactness principle for mixed local and nonlocal operators. This result is combined with Ricceri's variational principle to obtain an existence result for quasilinear elliptic problems under different growth assumptions on the nonlinearity. Furthermore, we apply the classical mountain pass theorem to obtain a second existence result in the superlinear case.

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Yergen Aikyn, Sekhar Ghosh, Vishvesh Kumar, Michael Ruzhansky. 2026-06-28. Mixed local-nonlocal quasilinear problems with mixed interpolated Hardy potential. https://arxiv.org/abs/2606.29348

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