# Multi-point boundary value problems for one-dimensionalp-Laplacian at resonance

Research paper by Youyu Wang, Guosheng Zhang, Weigao Ge

Indexed on: 01 Sep '06Published on: 01 Sep '06Published in: Journal of Applied Mathematics and Computing

#### Abstract

In this paper, we consider the multi-point boundary value problems for one-dimensional p-Laplacian at resonance:$$(\phi _p (x'(t)))' = f(t,x(t),x'(t))$$ subject to the boundary value conditions:$$(\phi _p (x'(0)) = \sum\limits_{i = 1}^{n - 2} {\alpha _i \phi _p (x'(\xi _i ))}$$,$$(\phi _p (x'(1)) = \sum\limits_{j = 1}^{m - 2} {\beta _j \phi _p (x'(\eta _i ))}$$ where ϕp(s)=|s|p-2s, p>1,αi(1≤i≤n-2)∈R,β{jit}(1≤j≤m-2)∈R, 0<ξ1<ξ2<...<ξn-2<1, 0<η1<η2<...<ηm-2<1, By applying the extension of Mawhin’s continuation theorem, we prove the existence of at least one solution. Our result is new.