Abstract
We considering the problem of solving a nonlinear differential equation in the Banach space of real functions and continuous on a bounded and closed interval. By means of the fixed point theory for a strict set contraction operator, this paper investigates the existence, nonexistence, and multiplicity of positive solutions for a nonlinear higher order boundary value problem.
Highlights
IntroductionWe considering the problem of solving a nonlinear differential equation of nth order
In the current paper, we considering the problem of solving a nonlinear differential equation of nth order
In This Paper we investigated the existence, nonexistence, and multiplicity of positive solutions for a nonlinear higher order boundary value problem on a bounded and closed interval by means of the fixed point theory for a strict set contraction operator
Summary
We considering the problem of solving a nonlinear differential equation of nth order. Let us mention that the theory of nonlinear differential equations has many useful applications in describing numerous events and problems of the real world. The existence results of positive solutions for integer order differential equations have been studied by several researchers (see [6,7,8,9] and the references therein), but, as far as we know, only a few papers consider the BVP for higher order nonlinear differential equations in Banach space of real functions and continuous on a bounded and closed interval, (see [1, 3, 5], and the references therein), So, the aim of this paper is to fill this gap.
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