컨텐츠 시작
학술대회/행사
초록검색
| 제출번호(No.) | 0547 |
|---|---|
| 분류(Section) | Contributed Talk |
| 분과(Session) | Variational Methods in Nonlinear Problems (SS-15) |
| 영문제목 (Title(Eng.)) |
The existence of three solutions for p-Laplacian problem on exterior domain |
| 저자(Author(s)) |
Seong-Uk Kim2, Eun Kyoung Lee1, Yong-Hoon Lee1 Pusan National University1, University of Alabama at Birmingham2 |
| 초록본문(Abstract) | This is a joint work with Seong-Uk Kim and Yong-Hoon Lee. In this talk, we prove the exisitence of three positive radial solutions of the following p-Laplacian problem on exterior domain for certain range of $\lambda$. \begin{equation*}\tag{$P_E$} \begin{cases} \mbox{div} \left(|\nabla u|^{p-2} \nabla u \right) + \lambda K_1(|x|)f(u) = 0, \\ u(x)=0,~~~~~~~~~~~~~~~~\mbox{if} ~~ |x|=r_0 \\ u(x)\to 0, ~~~~~~~~~~\mbox{if} ~~ |x| \to \infty \end{cases} \end{equation*} where $\Omega = \{x \in \mathbb{R}^N : |x| > r_0 \}, ~r_0>0, ~N>p>1,$ $f\in C([0,\infty), (0, \infty))$ is nondecreasing and $\lim_{u \to \infty} \frac{f(u)}{u^{p-1}} = 0.$ $K \in C((r_0,\infty),~ (0,\infty))$ satisfying $$\int_{r_0} ^{\infty} \varphi_p ^{-1} ( \tau ^{1-N} \int^\tau _{r_0} r^{N-1} K(r)dr )d\tau < \infty.$$ Moreover, we assume that there exist $a>0$ and $b>0$ such that $a<b$ and $$\frac{a^{p-1}}{f(a)} > C \frac{b^{p-1}}{f(b)},\qquad \mbox{when} \ \ C= 4^p \frac{\|e\|_\infty ^{p-1}}{\underline{h}}.$$ To prove this theorem, we prove the three solutions theorem for p-Laplacian ordianry differential problem with singular weight function. |
| 분류기호 (MSC number(s)) |
35J55 |
| 키워드(Keyword(s)) | three solutions theorem, upper and lower solution, Leray Schauder degree |
| 강연 형태 (Language of Session (Talk)) |
English |