Abstract
In this work, we investigate the existence of solutions for the particular type of the eighth-order boundary value problem. We prove our results using classical version of Leray–Schauder nonlinear alternative fixed point theorem. Also we produce a few examples to illustrate our results.
Highlights
Eighth-order differential equations govern the physics of some hydrodynamic stability problems
When the instability sets in as overstability, the problem is modeled by an eighth-order ordinary differential equation for which the existence and uniqueness of the solution can be found in the book [2]
We investigate the existence of solutions for the eighth-order boundary value problem
Summary
Eighth-order differential equations govern the physics of some hydrodynamic stability problems. Ballem and Kasi Viswanadham [5] presented a simple finite element method which involves the Galerkin approach with septic B-splines as basis functions to solve the eighth- order two-point boundary value problems. Guo–Krasnosel’skii fixed point theorem to solve the higher-order nonlinear boundary value problem. Graef et al [7] used various fixed point theorems to give some existence results for a nonlinear nth-order boundary value problem with nonlocal conditions. Kasi Viswanadham and Ballem [9] presented a finite element method involving the Galerkin method with quintic B-splines as basis functions to solve a general eighth-order two-point boundary value problem. Ahmad and Ntouyas [24] conferred some existence results based on some standard fixed point theorems and Leray–Schauder degree theory for an nth-order nonlinear differential equation with four-point nonlocal integral boundary conditions.
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