Positive solutions of a Lidstone boundary value problem with variable coefficient function |
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Authors: | Yun-Rui Yang Sui Sun Cheng |
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Institution: | 1. School of Mathematics, Physics and Software Engineering, Lanzhou Jiaotong University, Lanzhou, Gansu, 730070, People’s Republic of China 2. Department of Mathematics, Tsing Hua University, Hsinchu, Taiwan, R.O. China
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Abstract: | We establish the existence of positive solutions of the Lidstone boundary value problem $$\begin{array}{rcl}(-1)^{n}u^{(2n)}&=&\lambda a(t)f(u),\quad 0<t<1,\\3pt]u^{(2i)}(0)&=&u^{(2i)}(1)=0,\quad 0\leq i\leq n-1\end{array}$$ for all sufficiently small positive real λ, where the function a may change sign in 0,1] and the function f:0,∞)→R satisfies f(0)>0. We also show that our assumption is not vacuous. |
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