Prefer a chat interface with context about you and your work?
Existence and uniqueness results on Single-Peaked solutions of a semilinear problem
A one to one correspondence is established between the nondegenerate critical points of Q(x) in Ω and single peaked solutions of the problem \begin{cases} - \epsilon^{2}\Delta u + u = Q\left(x\right)u^{p - 1} & \text{in }\Omega \\ u > 0& \text{in }\Omega \text{ and }\\ u = 0 & \text{on …