We are concerned with the existence of blowing-up solutions to the following boundary value problem: -& UDelta;v = lambda V(x)e(v) in B-1, v = 0 on partial differential B-1, where B-1 is the unit ball in R-2, V(x) is a positive smooth potential, and lambda > 0 is a small parameter. We assume that the potential V satisfies some suitable assumptions in terms of the second and the fourth derivatives at 0, and we find a solution that exhibits a non-symmetric blow-up profile as lambda & RARR; 0(+).
D'Aprile, T.c. (2022). Non-symmetric blowing-up solutions for a class of Liouville equations in the ball. JOURNAL OF MATHEMATICAL PHYSICS, 63(2) [10.1063/5.0064197].
Non-symmetric blowing-up solutions for a class of Liouville equations in the ball
Teresa D'Aprile
2022-01-01
Abstract
We are concerned with the existence of blowing-up solutions to the following boundary value problem: -& UDelta;v = lambda V(x)e(v) in B-1, v = 0 on partial differential B-1, where B-1 is the unit ball in R-2, V(x) is a positive smooth potential, and lambda > 0 is a small parameter. We assume that the potential V satisfies some suitable assumptions in terms of the second and the fourth derivatives at 0, and we find a solution that exhibits a non-symmetric blow-up profile as lambda & RARR; 0(+).| File | Dimensione | Formato | |
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