On Some Problems With Nonlocal Integral Condition

Abstract

Abstract. We study the second order nonlinear boundary value problems with nonlocal integral conditions and construct the Fučík type spectrum for these problems.

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 spectrum of problem (1), (4) was given in [9]. 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].…”

On Fučík type spectrum for problem with integral nonlocal boundary condition

“…The Fučík type problem (1)- (2) with condition x(1) = γ 1 0 x(s) ds instead of condition (3) was analyzed in [10]. Graphical view of the spectrum of this problem shown in Fig.…”

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.…”