Invariance of Critical Points Under Kelvin Transform and Multiple Solutions in Exterior Domains of R2
Calculus of Variations and Partial Differential Equations
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Let Ω=R2∖B(0,1) be the exterior of the closed unit ball. We prove the existence of extremal constant-sign solutions as well as sign-changing solutions of the following boundary value problem −Δu=a(x)f(u) in Ω,u=0 on ∂Ω=∂B(0,1), where the nonnegative coefficient a satisfies a certain integrability condition. We are looking for solutions in the space D1,20(Ω) which is the completion of C∞c(Ω) with respect to the ∥∇⋅∥2,Ω -norm. Unlike in the situation of RN with... (See abstract in article).
Applied Mathematics | Mathematics | Partial Differential Equations
Costa, D. G.,
Invariance of Critical Points Under Kelvin Transform and Multiple Solutions in Exterior Domains of R2.
Calculus of Variations and Partial Differential Equations, 58(65),