Multiple Nontrivial Solutions for a Nonlocal Problem with Sublinear Nonlinearity

Zhigao Shi and Xiaotao Qian

Advances in Mathematical Physics, 2021, vol. 2021, issue 1

Abstract: In this paper, we study the following nonlocal problem −a−b∫Ω ∇u2dxΔu=λu+fxup−2u,x∈Ω,u=0,x∈∂Ω, where a, b > 0 are constants, 1 0, f ∈ L∞(Ω) is a positive function, and Ω is a smooth bounded domain in ℝN with N ≥ 3. By variational methods, we obtain a pair of nontrivial solutions for the considered problem provided |f|∞ is small enough.

Date: 2021
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https://doi.org/10.1155/2021/6671882

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlamp:v:2021:y:2021:i:1:n:6671882

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