On Solvability of the Damped Fučík Type Problem With Integral Condition

Abstract

The solvability results are established for the boundary value problem with a damping term, h is a bounded nonlinearity, µ, λ real parameters. The existence results are based of the knowledge of the Fučík type spectrum for the problem with h ≡ 0.

Boundary value problem with integral condition for a Blasius type equation

“…Consider a solution x(t, γ) of initial value problem (5), (7). If γ > 0, then x (t, γ) and x(t, γ) are positive and increasing functions for ) If x(t, γ) is a solution of initial value problem (5), (7) with γ > 0, then x(t, γ) is defined for all t 0 (t γ = ∞). ) Consider a solution x(t, γ) of initial value problem (5), (7).…”

“…If γ > 0, then x (t, γ) and x(t, γ) are positive and increasing functions for ) If x(t, γ) is a solution of initial value problem (5), (7) with γ > 0, then x(t, γ) is defined for all t 0 (t γ = ∞). ) Consider a solution x(t, γ) of initial value problem (5), (7). If γ > 0, then there exists a positive constant k such that lim t→+∞ x (t, γ) = k.…”

“…A survey of recent results on the Green's functions and on spectrum for stationary problems with nonlocal boundary conditions was provided by Štikonas in [9]. The second-order boundary value problem with a damping term subject to the integral conditions was considered by Sergejeva in [7]. The author has established the solvability results based on the knowledge of the Fučík type spectrum for the auxiliary problem.…”

“…The paper is organized as follows. In Section 2, we consider the properties of solutions of initial value problem (5), (7). Section 3 is devoted to the dependence of solutions on initial data.…”

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).…”