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Positive solution of singular Dirichlet boundary value problems for second order differential equation system |
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| Authors: | Zhongli Wei |
| Affiliation: | a Department of Mathematics, Shandong Jianzhu University, Jinan, Shandong 250014, People's Republic of China b School of Mathematics and System Sciences, Shandong University, Jinan, Shandong 250100, People's Republic of China |
| Abstract: | This paper investigates the existence of positive solutions of singular Dirichlet boundary value problems for second order differential system. A necessary and sufficient condition for the existence of C[0,1]×C[0,1] positive solutions as well as C1[0,1]×C1[0,1] positive solutions is given by means of the method of lower and upper solutions and the fixed point theorems. Our nonlinearity fi(t,x1,x2) may be singular at x1=0, x2=0, t=0 and/or t=1, i=1,2. |
| Keywords: | Singular Dirichlet boundary value problem Positive solution Lower and upper solutions Differential system |
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