Infinitely many sign-changing solutions for concave-convex elliptic problem with nonlinear boundary condition

• Main Authors: Li Wang, Peihao Zhao
• Format: Article
• Language: English
• Published: Texas State University 2015-10-01
• Series: Electronic Journal of Differential Equations
• Subjects: Nonlinear boundary condition; concave-convex; invariant sets; sign-changing solutions
• Online Access: http://ejde.math.txstate.edu/Volumes/2015/266/abstr.html

In this article, we study the existence of sign-changing solutions to $$\displaylines{ -\Delta u+u =|u|^{p-1}u\quad \text{in } \Omega \cr \frac{\partial u}{\partial n}=\lambda |u|^{q-1}u\quad \text{on }\partial \Omega }$$ with $0<q<1<p\leq \frac{N+2}{N-2}$ and $\lambda>0$. By using a combination of invariant sets and Ljusternik-Schnirelman type minimax method, we obtain two sequences of sign-changing solutions when p is subcritical and one sequence of sign-changing solutions when p is critical.