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

2025/03/01 by Dhanya, R., Giacomoni, Jacques, Jana, Ritabrata · 2 citations
#35J20 #35J25 #35J60 #35J92 #35R11 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2503.00365

Abstract

In this article we examine the multiplicity of non-negative solutions to mixed local-nonlocal equations involving \((-Δ_p) + (-Δ^s_q)\) in a bounded smooth domain. The nonlinearity incorporates a parameter \(λ> 0\), 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 \(λ\) by analyzing the associated generalized eigenvalue problem.

Cited by

• Mixed double phase equations with local and nonlocal operators
• Multiplicity results for mixed local-nonlocal variable exponent problem involving singular and superlinear term

Related

• Multiplicity result for mixed local and nonlocal Kirchhoff problem involving critical growth
• Multiplicity results for mixed local-nonlocal variable exponent problem involving singular and superlinear term
• Quasilinear problems with mixed local-nonlocal operator and concave-critical nonlinearities: Multiplicity of positive solutions
• Mixed local-nonlocal equations with critical nonlinearity on ℝ^N: Non-existence, Existence, and Multiplicity of positive solutions
• Mixed local-nonlocal quasilinear problems with critical nonlinearities