Existence result for a third-order ODE with nonlinear boundary conditions in presence of a sign-type Nagumo control

Abstract

In this work we provide an existence and location result for the third-order nonlinear differential equationwhere f : [a, b] × R 3 → R is a continuous function, and two types of boundary conditions:with φ, ψ : R 2 → R continuous functions, monotonous in the second variable and A, B, C ∈ R.

A Fourth-Order Boundary Value Problem with One-Sided Nagumo Condition

“…For more related works, interested readers may refer to 1-14 . The one-sided Nagumo-type condition brings some difficulties in studying this kind of problem, as it can be seen in [15][16][17][18] . Motivated by the above works, we consider the existence of solutions when f satisfies one-sided Nagumo-type conditions.…”

Existence and Iteration of Positive Solutions to Third-Order BVP for a Class ofp-Laplacian Dynamic Equations on Time Scales

“…On the one hand, higher-order nonlinear boundary value problems have been studied extensively; for details, see [4,10,17,18] and references therein. On the other hand, the boundary value problems with -Laplacian operator have also been discussed extensively in the literature; for example, see [3, 7-9, 11, 19-21].…”

Solvability of a nonlinear third-order periodic boundary value problem

“…So the third-order boundary value problems were discussed by many authors and many good results have been obtained in recent years, for instance, see [2][3][4][5][6][7][8][9][10][11][12][13][14] and the references therein. However, most of the boundary conditions in the above mentioned references are two-point or three-point boundary conditions, the periodic boundary conditions are quite rarely seen [2,5,[9][10][11][12]14].…”