We prove the existence of entire solutions with exponential growth for the semilinear elliptic system -Δu = -uv2 in ℝN, -Δv = -u2v in ℝN,u,u > 0, 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 lim d→+∞ [(1+z/d)]= ex sin y in the present setting. © 2014 IOP Publishing Ltd & London Mathematical Society.
Entire solutions with exponential growth for an elliptic system modelling phase separation
SOAVE, NICOLA;ZILIO, ALESSANDRO
2014-01-01
Abstract
We prove the existence of entire solutions with exponential growth for the semilinear elliptic system -Δu = -uv2 in ℝN, -Δv = -u2v in ℝN,u,u > 0, 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 lim d→+∞ [(1+z/d)]= ex sin y in the present setting. © 2014 IOP Publishing Ltd & London Mathematical Society.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
