Boundary value problems for general discrete systems on infinite intervals

Boundary Value Problems for Functional Difference Equations on Infinite Intervals

Some Boundary Value Problems on Infinite Intervals for Functional Differential Systems

< +∞. (3) Earlier, these problems were studied only in the cases, where f1 and f2 are either the Nemytski’s operators ([3], [4], [5]), or the linear operators ([1], [2], [6]). Below, we will present new, and in a certain sense, unimprovable conditions which guarantee, respectively, the solvability and well-posedness of (1), (2) and (1), (3). Throughout the paper, the following notation will be ...

Existence of Multiple Solutions for Three-point Boundary-value Problems on Infinite Intervals in Banach Spaces

We prove the existence of at least three solutions for a secondorder three-point boundary-value problem on infinite intervals in Banach spaces. We use the unbounded upper and lower solution method, and the topological degree theory of strict-set-contractions. To illustrate our results, we present an example.

Multiple Positive Solutions for Singular Boundary-value Problems with Derivative Dependence on Finite and Infinite Intervals

In this paper, Krasnoselskii’s theorem and the fixed point theorem of cone expansion and compression are improved. Using the results obtained, we establish the existence of multiple positive solutions for the singular second-order boundary-value problems with derivative dependance on finite and infinite intervals.

Existence of positive solutions for multi-point boundary value problems on infinite intervals in Banach spaces

{ (−1)u(x) = λp(x)f(u(x)), 0 < x < 1 u(0) = ∑m j=1 aju (ηj), u (1) = ∑m j=1 bju (ηj), i = 0, 1, . . . , n− 1 where aj , bj ∈ [0,∞), j = 1, 2, . . . ,m, with 0 < ∑m j=1 aj < 1, 0 < ∑m j=1 bj < 1, and ηj ∈ (0, 1) with 0 < η1 < η2 < . . . < ηm < 1, under certain conditions on f and p using the Krasnosel’skii fixed point theorem for certain values of λ. We use the positivity of the Green’s function...