Invariance of Critical Points Under Kelvin Transform and Multiple Solutions in Exterior Domains of R2

Authors

Siegfried Carl, Martin-Luther-University Halle-WittenbergFollow
David G. Costa, University of Nevada, Las VegasFollow
Morteza Fotouhi, Sharif University of Technology
Hossein Tehrani, University of Nevada, Las VegasFollow

Document Type

Article

Publication Date

3-20-2019

Publication Title

Calculus of Variations and Partial Differential Equations

Volume

58

Issue

65

First page number:

1

Last page number:

24

Abstract

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).

Disciplines

Applied Mathematics | Mathematics | Partial Differential Equations

Language

English

Repository Citation

Carl, S., Costa, D. G., Fotouhi, M., Tehrani, H. (2019). Invariance of Critical Points Under Kelvin Transform and Multiple Solutions in Exterior Domains of R2. Calculus of Variations and Partial Differential Equations, 58(65), 1-24.
http://dx.doi.org/10.1007/s00526-019-1519-y