The Existence, Uniqueness, and Multiplicity of Solutions for Two Fractional Nonlocal Equations
Author:
Wang YueORCID,
Wei Wei,
Zhou Ying
Abstract
This paper establishes the existence of unique and multiple solutions to two nonlocal equations with fractional operators. The main results are obtained using the variational method and algebraic analysis. The conclusion is that there exists a constant λ*>0 such that the equations have only three, two, and one solution, respectively, for λ∈(0,λ*), λ=λ*, and λ>λ*. The main conclusions fill the gap in the knowledge of this kind of fractional-order problem.
Funder
Foundation of Research Project for Graduate of Guizhou Province
National Natural Science Foundation of China
Subject
Geometry and Topology,Logic,Mathematical Physics,Algebra and Number Theory,Analysis
Reference56 articles.
1. Hitchhiker’s guide to the fractional Sobolev spaces;Nezza;Bull. Sci. Math.,2012
2. Boundary values of functions with finite Dirichlet integral;Aronszajn;Technol. Rep. Univ. Kans.,1955
3. Proprietà di alcune classi di funzioni in più variabili;Gagliardo;Ricerche. Mat.,1958
4. Generalized Sobolev spaces and their applications to boundary value problems of partial differential equations;Slobodeckij;Leningrad. Gos. Ped. Inst. Učep. Zap.,1958
5. Fractional Hardy-Sobolev elliptic problems;Yang;Topol. Methods Nonlinear Anal.,2020
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