Existence Theory for Nonlinear Third-Order Ordinary Differential Equations with Nonlocal Multi-Point and Multi-Strip Boundary Conditions

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.

A Self-Adjoint Coupled System of Nonlinear Ordinary Differential Equations with Nonlocal Multi-Point Boundary Conditions on an Arbitrary Domain

“…Evidently, the condition (A 2 ) is satisfied. Thus, the conclusion of Theorem 2 applies to the system (27) with boundary conditions (26). So, there exists a solution of the problem (27)…”

“…Modern tools (variational and topological methods) of functional analysis play an important role in establishing the existence theory for nonlinear boundary value problems [24,25]. For the application of the fixed-point theory to single-valued and multi-valued boundary value problems of ordinary differential equations, for instance, see [26,27] and the references cited therein.…”

A Study on the New Class of Inequalities of Midpoint-Type and Trapezoidal-Type Based on Twice Differentiable Functions with Conformable Operators

“…Mathematical modeling is one of the most important fields of this theory in which fractional operators are defined to design different fractional differential equations for describing the phenomena. For instance, one can mention to the thirdorder BVP with multistrip multipoint conditions [1], hybrid version and the Hilfer type of thermostat model [2,3], fractional HIV model with the Mittag-Leffler-type kernel [4], mathematical fractional model of Q fever [5], fractional dynamics of mumps virus [6], fractional p-Laplacian equa-tions [7], fractal-fractional version of AH1N1/09 virus along with the fractional Caputo-type version [8], etc.…”

Numerical solution of system of Fredholm-Volterra integro-differential equations using Legendre polynomials

“…Abbasbandy and Taati [7] have solved the system of nonlinear Volterra-integro-differential equations using the operational Tau method. Srivastava [8] investigated the existence theory for nonlinear third-order ordinary differential equations with nonlocal multi-point and multi-strip boundary conditions. Javidi [9] presented a modified homotopy perturbation method for solving system of linear Fredholm integral equations.…”