On solvability of second-order Sturm-Liouville boundary value problems at resonance期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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On solvability of second-order Sturm-Liouville boundary value problems at resonance

Authors:	Dong Yujun

Institution:	Institute of Mathematics, Jilin University, Changchun, Jilin, 130023, People's Republic of China

Abstract:	In this paper, based on of the concept $q_0\in H_0(p,(0,1),\alpha,\beta)$ , which is a generalized form of the first resonant point $\pi^2$ to the Picard problem $x'+\lambda x=0$ , , we study the solvability of second-order Sturm-Liouville boundary value problems at resonance , $x(0){\cos \alpha}-p(0)x'(0)\sin \alpha=0$ , $x(1)\cos \beta-p(1)x'(1)\sin \beta=0$ , and improve the previous results about problems $x'+\pi^2x+g(t,x)=h(t),x(0)=x(1)=0$ derived by Chaitan P. Gupta, R.Iannacci and M. N. Nkashama, and Ma Ruyun, respectively.

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