The method of lower and upper solutions for third order singular four point boundary value problems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

The method of lower and upper solutions for third order singular four point boundary value problems

Authors:	Jian Zhang Zhongli Wei Wei Dong

Affiliation:	1. School of Mathematics and System Sciences, Shandong University, Jinan, Shandong, 250100, People’s Republic of China 2. Department of Mathematics, Shandong Jianzhu University, Jinan, Shandong, 250101, People’s Republic of China 3. Hebei University of Engineering, Handan, Hebei, 056021, China

Abstract:	We mainly study the existence of positive solutions for the following third order singular four point boundary value problem $$begin{cases}x^{(3)}(t)+f(t,x,x',-x'')=0,quad 0α<1, 0≤β<1, 0<ξ<1,0<η<1. And we obtain some necessary and sufficient conditions for the existence of C ²[0,1] positive solutions by means of the lower and upper solution method. Our nonlinearity f(t,x,y,z) may be singular at x,y,z,t=0 and/or t=1.

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