Geometry of phase space and solutions of semilinear elliptic equations in a ball

By Jean Dolbeault, I. Flores. 2007

51 citations recorded by the source corpus.

We consider the problem {-Δu=u p +λu in in B, u>0 in B, u=0 on ∂B, where B denotes the unit ball in R N , N > 3, A > 0 and p > 1. Merle and Peletier showed that for p > N+2/N-2 there is a unique value A = λ* > 0 such that a radial singular solution exists. This value is the only one at which an unbounded sequence of classical solutions of (1) may accumulate. Here we prove that if additionally p 0 0 in B, u = 0 on ∂B, where f(s) = s p + s q , 1 < q < p, and p satisfies the same condition as above.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/f39a1c2ae1beb436eabd8bd8b7745358355baba2

Citations in the corpus

• Multiplicity of solutions for a fourth order equation with power-type nonlinearity (2010, unknown): “This idea traces back to the work of Bamón, Flores, del Pino [3] and was subsequently applied also in [17–19].”