Abstract
We investigate the solvability and Ulam stability for a nonlocal nonlinear third-order integro-multi-point boundary value problem on an arbitrary domain. The nonlinearity in the third-order ordinary differential equation involves the unknown function together with its first- and second-order derivatives. Our main results rely on the modern tools of functional analysis and are well illustrated with the aid of examples. An analogue problem involving non-separated integro-multi-point boundary conditions is also discussed.
Highlights
IntroductionWe study Equation (1) with the following type non-separated boundary conditions: α1 u ( a ) + α2 u ( T ) =
Consider a third-order ordinary differential equation of the form: u000 (t) = f (t, u(t), u0 (t), u00 (t)), a < t < T, a, T ∈ R, (1)supplemented with the boundary conditions: Z T a a u(s)ds = u0 (s)ds = u00 (s)ds =m p j =1 m i =1 p∑ γj u(σj ) + ∑ ξ i Z ρ i +1∑ μ j u0 + ∑ ηi
In [2], the authors studied the existence of solutions for third-order nonlinear boundary value problems arising in nano-boundary layer fluid flows over stretching surfaces
Summary
We study Equation (1) with the following type non-separated boundary conditions: α1 u ( a ) + α2 u ( T ) =. Nonlinear third-order ordinary differential equations frequently appear in the study of applied problems. In [2], the authors studied the existence of solutions for third-order nonlinear boundary value problems arising in nano-boundary layer fluid flows over stretching surfaces. The investigation of the model of magnetohydrodynamic flow of second grade nanofluid over a nonlinear stretching sheet is based on a nonlinear third-order ordinary differential equation [4]. For the recent development of the boundary value problems involving integral and multi-strip conditions, we refer the reader to the works [14,15,16,17,18,19]. It is imperative to mention that the results obtained in this paper are new and yield several new results as special cases for appropriate choices of the parameters involved in the problems at hand
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