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ZJUS-A
Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering)  2004, Vol. 5 Issue (3): 353-357    DOI: 10.1631/jzus.2004.0353
Mathematics     
Existence of solutions and positive solutions to a fourth-order two-point BVP with second derivative
YAO Qing-liu
Department of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing 210003, China
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Abstract  Several existence theorems were established for a nonlinear fourth-order two-point boundary value problem with second derivative by using Leray-Schauder fixed point theorem, equivalent norm and technique on system of integral equations. The main conditions of our results are local. In other words, the existence of the solution can be determined by considering the “height” of the nonlinear term on a bounded set. This class of problems usually describes the equilibrium state of an elastic beam which is simply supported at both ends.

Key words： Nonlinear fourth-order equation      Two-point boundary value problem      Solution and positive solution      Existence      Fixed point theorem     
Received: 18 March 2003     
CLC:  O175.8  
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YAO Qing-liu. Existence of solutions and positive solutions to a fourth-order two-point BVP with second derivative. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2004, 5(3): 353-357.

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http://www.zjujournals.com/xueshu/zjus-a/10.1631/jzus.2004.0353     OR     http://www.zjujournals.com/xueshu/zjus-a/Y2004/V5/I3/353

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