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| POSITIVE SOLUTIONS TO A BVP WITH TWO INTEGRAL BOUNDARY CONDITIONS |
| Kaikai Liu,Yunrui Yang,Yang Yang |
| (School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070, Gansu, PR China) |
| DOI： |
| Abstract: |
| Based on the Guo-Krasnoselskii's fixed-point theorem, the existence and multiplicity of positive solutions to a boundary value problem (BVP) with two integral boundary conditions
\begin{equation*}
\left\{\hskip-1.5mm
\begin{array}{l}
v^{(4)}=f(s,v(s),v'(s),v''(s)),\quad s\in[0,1],\\[3pt]
v'(1)=v'''(1)=0,\\[4pt]
\displaystyle v(0)=\int_{0}^{1}g_1(\tau)v(\tau){\rm d}\tau,\quad v''(0)=\int_{0}^{1}g_2(\tau)v''(\tau){\rm d}\tau
\end{array}
\right.
\end{equation*}
are obtained, where $f,\ g_1,\ g_2$\ are all continuous. It generalizes the results of one positive solution to multiplicity and improves some results for integral BVPs. Moreover, some examples are also included to demonstrate our results as applications. |
| Key words: integral boundary conditions; positive solutions; cone |