Infinitely many sign-changing solutions for concave-convex elliptic problem with nonlinear boundary condition
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 usi...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2015-10-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2015/266/abstr.html |
| Summary: | 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. |
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| ISSN: | 1072-6691 |