| Existence of solutions and positive solutions to a fourth-order two-point BVP with second derivative |
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| 作者姓名： | 姚庆六 |
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| 作者单位： | Department of |
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| 摘 要： | ~~40,1]Csatisfyingand()hr ?*umu'k(mh r)and*uisanonnegativeconcavefunction.Moreover,ifoneofthefollowingconditionsissatisfied:(1)A B>0;(2)C D<0;(3)f(t,0,0) 0,0t1,then*u(t)>0,00suchthatmax{():01,0,80}64,rrr?#ft,u,vtuvthentheproblem(P)hasatleastonesolutionu*C40,1]satisfying*urand()*"u8randu*isanonnegativeconcavefunction.Moreover,iff(t,0,0) 0,0t1,thenu*(t)>0,0
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Existence of solutions and positive solutions to a fourth-order two-point BVP with second derivative |
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| YAO Qing-liu.Existence of solutions and positive solutions to a fourth-order two-point BVP with second derivative[J].Journal of Zhejiang University Science,2004(3). |
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| Authors: | YAO Qing-liu |
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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. |
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| Keywords: | Nonlinear fourth-order equation Two-point boundary value problem Solution and positive solution Existence Fixed point theorem |
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