The Regions of Solvability for Some Three Point Problem

Abstract

The solvability results are established for the boundary value problem , where x + = max{x, 0}, x - = max{-x, 0}, h is a bounded nonlinearity. The existence results are based of the knowledge of the spectrum for the problem with h ≡ 0.

The Fucík spectrum for nonlocal BVP with Sturm–Liouville boundary condition

“…But the notation F + 0,R,− refers to solutions of the equation x = −µx + + λx − without zeroes in the interval (0, 1) with µ ∈ R and λ < 0. Similar notations of the branches were used in the other author's works [10][11][12] devoted to the Fučík type problems with nonlocal (integral) condition.…”

“…The progress in this direction can be traced by [10] and [11]. Also another type of nonlocal boundary conditions was considered by the author in the work [12].…”

A survey on stationary problems, Green's functions and spectrum of Sturm–Liouville problem with nonlocal boundary conditions

“…Sergejeva investigated Fučìk type problem with Bitsadze-Samarskii type NBC [201] and with a damping term and integral type NBC [203]. Sajavičius in his doctoral dissertation [170] analysed numerical solution of PDEs with nonlocal conditions (stability of FDS, radial basis function method).…”

Positive Solutions for a Class of Fourth-Orderp-Laplacian Boundary Value Problem Involving Integral Conditions

“…where ( ) = | | −2 , > 1, = −1 , 1/ + 1/ = 1, ∈ 1 [0, 1] is symmetric on the interval [0, 1] (i.e., ( Boundary value problems of ordinary differential equations have become an important research field in recent years. Fourth-order -Laplacian boundary value problems arise in applied mathematics, physics, gas diffusion through porous media, engineering, elastic mechanics, electromagnetic waves of gravity driven flows, and the various areas of adiabatic tubular reactor processes, as well as biological problems; see [1][2][3][4][5] and the references therein.…”

“…In [2], by making use of the theory of the spectrum, Sergejeva studied the regions of solvability for three-point boundary value problem:…”