We establish existence of an infinite family of exponentially-decaying non-radial \(C^{2}\) solutions to the equation \(\Delta u+f(u)=0\) on \(\mathbb{R}^{2}\) for a large class of nonlinearities \(f\). These solutions have the form \(u(r, \theta)=e^{\text {imit }} u(r)\), where \(r\) and \(\theta\)
Continuity in two dimensions for a very degenerate elliptic equation
โ Scribed by Filippo Santambrogio; Vincenzo Vespri
- Publisher
- Elsevier Science
- Year
- 2010
- Tongue
- English
- Weight
- 351 KB
- Volume
- 73
- Category
- Article
- ISSN
- 0362-546X
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