Abstract
Fourth order boundary value problems arise in the study of the equilibrium of an elastaic beam under an external load. The author earlier investigated the existence and uniqueness of the solutions of the nonlinear analogues of fourth order boundary value problems that arise in the equilibrium of an elastic beam depending on how the ends of the beam are supported. This paper concerns the existence and uniqueness of solutions of the fourth order boundary value problems with periodic boundary conditions.
Highlights
Fourth order boundary value problems arise in the study of the equilibrium of an elastic beam under an external load, where the existence, uniqueness and iterative methods to construct the solutions have been studied extensively
The purpose of this paper is to study the fourth order boundary value problem with periodic boundary conditions:
We note that the fourth order linear eigenvalue problem u(0) u(2;[) u’(0) u’(2n) u"(0) u"(2n) u"(0) u’" (2n) O, has nn
Summary
Fourth order boundary value problems arise in the study of the equilibrium of an elastic beam under an external load, (e.g., see [I], [2], [3]) where the existence, uniqueness and iterative methods to construct the solutions have been studied extensively. 0- To prove the existence of a solution for the boundary value problem d4u 4 cu’ + g(x u) e(x) dx x [0 2,t] - YI the linear boundary value problem d4u + au’ h(x), x dx u(O) u(2n), u’(O)
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