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arXiv · 2503.00365

Multiplicity Results for Mixed Local Nonlocal Equations With Indefinite Concave-Convex Type Nonlinearity

R. Dhanya·Jacques Giacomoni·Ritabrata Jana
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Abstract

In this article we examine the multiplicity of non-negative solutions to mixed local-nonlocal equations involving \((-\Delta_p) + (-\Delta^{s}_{q})\) in a bounded smooth domain. The nonlinearity incorporates a parameter \(\lambda > 0\), a sublinear term, and a superlinear term, with sign-changing weight functions \(a(x)\) and \(b(x)\). Under suitable conditions, we establish the existence of at least two distinct nontrivial non-negative solutions in both the subcritical and critical regimes via fibering map analysis and constrained minimization on the Nehari manifold. Additionally, for \(p \not = q\), we obtain a nonexistence result for large \(\lambda\) by analyzing the associated generalized eigenvalue problem.

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R. Dhanya, Jacques Giacomoni, Ritabrata Jana. 2025-03-01. Multiplicity Results for Mixed Local Nonlocal Equations With Indefinite Concave-Convex Type Nonlinearity. https://arxiv.org/abs/2503.00365

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