Abstract
Under barrier strips type assumptions we study the existence of C 3 [ 0 , 1 ] —solutions to various two-point boundary value problems for the equation x ‴ = f ( t , x , x ′ , x ″ ) . We give also some results guaranteeing positive or non-negative, monotone, convex or concave solutions.
Highlights
We study the solvability of boundary value problems (BVPs) for the differential equation x 000 = f (t, x, x 0, x 00 ), t ∈ (0, 1), (1)
The solvability of BVPs for third-order differential equations has been investigated by many authors
We will cite papers devoted to two-point BVPs which are mostly with some of the above boundary conditions; in each of these works A, B, C = 0
Summary
We study the solvability of boundary value problems (BVPs) for the differential equation x 000 = f (t, x, x 0 , x 00 ), t ∈ (0, 1),. We will cite papers devoted to two-point BVPs which are mostly with some of the above boundary conditions; in each of these works A, B, C = 0 Such problems for equations of the form x 000 = f (t, x ), t ∈ (0, 1), have been studied by H. Preparing the application of Lemma 1, we impose conditions which ensure the a priori bounds from (iv) for the eventual C3 [0, 1] - solutions of the families of BVPs for (7)λ , λ ∈ [0, 1], with one of the boundary conditions (k), k = 2, 6.
Sign-in/Register to view highlights & summary 
Published Version (
Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call