Non‐linear boundary value problems on the semi‐infinite interval: an upper and lower solution approach

Abstract

Existence criteria are presented for non‐linear boundary value problems on the half line. In particular, the theory includes a problem in the theory of colloids and a problem arising in the unsteady flow of a gas through a semi‐infinite porous medium.

Nonlinear Boundary Value Problems on Semi-Infinite Intervals using Weighted Spaces: An Upper and Lower Solution Approach

“…In the literature there are several existence results for (1/p)(py ) + Φ(t) f (t, y) = 0, t ∈ (a, +∞) with y(a) = 0, lim t→+∞ p(t)y (t) = 0; see [3,4,6,8,9,10,11,12,17,21,22,23,24,25] and the references therein. In [5,7] the authors discuss the existence of bounded solution for the equation (1/p)(py ) + Φ(t)f (t, y, py ) = 0, t ∈ (a, +∞) with some initial value condition. We refer the reader also to [1,2,13,14,15,16,18,17,18,19,20].…”

Boundary value problems on half‐line for second‐order nonlinear impulsive differential equations

“…Boundary value problems (BVPs) on infinite intervals have been studied extensively due to fact that they naturally arise in heat conduction, chemical engineering, underground water flow, thermo-elasticity, and plasma physics problems; see previous studies [1][2][3][4][5][6][7][8] for equations without impulse and with impulse. [9][10][11] Most of the results are obtained for the existence of the bounded or positive solutions by using upper and lower solution method, monotone iterative technique, and applying fixed point index theorem on cone and operator spectra theorem.…”

Solvability for integral boundary value problems of fractional differential equation on infinite intervals

“…More examples and a collection of works on the existence of solutions of Boundary value problems on infinite intervals for differential, difference and integral equations may be found in the monographs [1,15]. For some works and various techniques dealing with such boundary value problems, see [2,5,7,13,21,22,23,26] and the references therein.…”