Multiplicity of solutions to nearly critical elliptic equation in the bounded domain of R-3

作者：Chen, Wenjing; Guerra, Ignacio^*

来源：Journal of Mathematical Analysis and Applications, 2015, 424(1): 179-200.

DOI：10.1016/j.jmaa.2014.11.019

• Multiplicity
• Bubble solutions
• Mountain pass solution

We consider the following Dirichlet boundary value problem
{-Delta u = u(5-epsilon) + lambda u(q), u > 0 in Omega;
u = 0 on partial derivative Omega, (0.1)
where Omega is a smooth bounded domain in R-3, 1 < q < 3, the parameters lambda > 0 and epsilon > 0. By Lyapunov-Schmidt reduction method and the Mountain Pass Theorem, we prove that in suitable ranges for the parameters lambda and epsilon, problem (0.1) has at least two solutions. Additionally if 2 <= q < 3, we prove the existence of at least three solutions. Consequently, we prove a non-uniqueness result for a suberitical problem with an increasing nonlinearity.

• 出版日期2015-4-1
• 单位西南大学