On weakly nonlinear boundary value problems on infinite intervals

Boundary Value Problems for Functional Difference Equations on Infinite Intervals

Computation of Positive Solutions for Nonlinear Impulsive Integral Boundary Value Problems with p-Laplacian on Infinite Intervals

and Applied Analysis 3 2. Preliminaries and Several Lemmas Definition 1. LetE be a real Banach space. A nonempty closed set P ⊂ E is said to be a cone provided that (1) au + bv ∈ P for all u, v ∈ P and all a ≥ 0, b ≥ 0, (2) u, −u ∈ P implies that u = 0. Definition 2. A map α : P → [0, +∞) is said to be concave on P, if α(tu + (1 − t)v) ≥ tα(u) + (1 − t)α(v) for all u, v ∈ P and t ∈ [0, 1]. Let ...

Boundary-Value Problems for Weakly Nonlinear Delay Differential Systems

and Applied Analysis 3 where the kernel K t, s is an n × n Cauchy matrix defined in the square a, b × a, b being, for every fixed s ≤ t , a solution of the matrix Cauchy problem LK ·, s t : ∂K t, s ∂t −A t Sh0K ·, s t Θ, K s, s I, 1.8 where K t, s ≡ Θ if a ≤ t < s ≤ b, Θ is n × n null matrix and I is n × n identity matrix. A fundamental n × n matrix X t for the homogeneous φ ≡ θ equation 1.5 ha...

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.

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 ...