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 ϕ p (s)=|s|p-2 s, 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.
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Supported by National Natural Sciences Foundation of China(10371006)
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Wang, Y., Zhang, G. & Ge, W. Multi-point boundary value problems for one-dimensionalp-Laplacian at resonance. J. Appl. Math. Comput. 22, 361–372 (2006). https://doi.org/10.1007/BF02896485
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DOI: https://doi.org/10.1007/BF02896485