Solvability of a three-point nonlinear boundary-value problem
Using the Leray Schauder nonlinear alternative, we prove the existence of a nontrivial solution for the three-point boundary-value problem $$displaylines{ u''+f(t,u)= 0,quad 0<t<1 cr u(0)= alpha u'(0),quad u(1)=eta u'(eta ), }$$ where $eta in (0,1)$, $alpha ,...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2010-09-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2010/139/abstr.html |
| Summary: | Using the Leray Schauder nonlinear alternative, we prove the existence of a nontrivial solution for the three-point boundary-value problem $$displaylines{ u''+f(t,u)= 0,quad 0<t<1 cr u(0)= alpha u'(0),quad u(1)=eta u'(eta ), }$$ where $eta in (0,1)$, $alpha ,eta in mathbb{R}$, $fin C([0,1] imesmathbb{R},mathbb{R})$. Some examples are given to illustrate the results obtained. |
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| ISSN: | 1072-6691 |