Year: 2014
Type: article
Abstract: We prove the existence of entire solutions with exponential growth for the semilinear elliptic system for every N ⩾ 2. Our construction is based on an approximation procedure, whose convergence is ensured by suitable Almgren-type monotonicity formulae. The construction of the resulting solutions is extended to systems with k components, for every k > 2; in this case, the proof is much more involved and is achieved by approximation of solutions with exponential growth by means of solutions with algebraic growth of increasing degree, translating the limit in the present setting.
Source: Nonlinearity
Authors: Nicola Soave, Alessandro Zilio
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W1974975433