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arXiv · 2412.08427

Existence of solutions to a quasilinear nonlocal PDE

Lisbeth Carrero·Alexander Quaas·Andres Zuniga
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Abstract

In this paper, we introduce a new class of quasilinear operators, which represents a nonlocal version of the operator studied by Stuart and Zhou [1], inspired by models in nonlinear optics. We will study the existence of at least one or two solutions in the cone $X=\{u\in H^s_0(\Omega): u\geq 0\}$ using variational methods. For this purpose, we analyze two scenarios: the asymptotic sublinear and linear growth cases for the reaction term. Additionally, in the sublinear case, we establish a nonexistence result.

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Lisbeth Carrero, Alexander Quaas, Andres Zuniga. 2024-12-11. Existence of solutions to a quasilinear nonlocal PDE. https://arxiv.org/abs/2412.08427

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