Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
837037 | Nonlinear Analysis: Real World Applications | 2016 | 15 Pages |
Abstract
Using minimax methods and Lusternik–Schnirelmann theory, we study multiple positive solutions for the Schrödinger–Kirchhoff equation M(∫Ωλ|∇u|2dx+∫Ωλu2dx)[−Δu+u]=f(u)M(∫Ωλ|∇u|2dx+∫Ωλu2dx)[−Δu+u]=f(u) in Ωλ=λΩΩλ=λΩ. The set Ω⊂R3Ω⊂R3 is a smooth bounded domain, λ>0λ>0 is a parameter, MM is a general continuous function and ff is a superlinear continuous function with subcritical growth. Our main result relates, for large values of λλ, the number of solutions with the least number of closed and contractible in Ω¯ which cover Ω¯.
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Authors
João R. Santos Junior,