|
| MULTIPLE POSITIVE SOLUTIONS FOR A CLASS OF INTEGRAL BOUNDARY VALUE PROBLEM |
| Yang Yang,Yunrui Yang,Kepan Liu |
| (School of Math. and Physics, Lanzhou Jiaotong University, Lanzhou 730070, Gansu, PR China) |
| DOI： |
| Abstract: |
| In this paper, the existence and multiplicity of positive solutions for a class of non-resonant fourth-order integral boundary value problem with two parameters are established by using the Guo-Krasnoselskii's fixed-point theorem, where $f\hskip-0.4mm \in\hskip-0.4mm C\left([0,1]\hskip-0.4mm \times\hskip-0.4mm [0,+\infty)\hskip-0.4mm \times\hskip-0.4mm (-\infty,0],[0,+\infty) \right)$, $q(t)\hskip-0.4mm \in\hskip-0.4mm L^1[0,1]$ is nonnegative, $\alpha,\beta\in R$ and satisfy $\beta<2\pi^2$, $\alpha>0$, $\alpha/\pi^4+\beta/\pi^2<1$, $\lambda_{1,2}=(-\beta\mp\sqrt{\beta^2+4\alpha}) /2$. The corresponding examples are raised to demonstrate the results we obtained. |
| Key words: positive solutions; fixed point; integral boundary conditions |