Existence and uniqueness for nonlinear boundary value problems on infinite intervals

Existence and Local Uniqueness for Nonlinear Lidstone Boundary Value Problems

Higher order upper and lower solutions are used to establish the existence and local uniqueness of solutions to y = f(t, y, y′′, . . . , y(2n−2)), satisfying boundary conditions of the form gi(y(0), y(2i−2)(1))−y(2i−2)(0) = 0, hi(y(0), y(2i−2)(1))−y(2i−2)(0) = 0, 1 ≤ i ≤ n.

Existence and uniqueness of solutions for p-laplacian fractional order boundary value problems

In this paper, we study sufficient conditions for existence and uniqueness of solutions of three point boundary vale problem for p-Laplacian fractional order differential equations. We use Schauder's fixed point theorem for existence of solutions and concavity of the operator for uniqueness of solution. We include some examples to show the applicability of our results.

Boundary Value Problems for Functional Difference Equations on Infinite Intervals

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.

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...