Abstract
This paper provides conditions for the existence of a solution to the second-order nonlinear boundary value problem on the half-line of the form with where , . To achieve our goal, we use Schauder’s fixed-point theorem and the perturbation technique for a Fredholm operator of index 0. Moreover, we construct the necessary condition for the existence of a solution to the considered problem.
Highlights
This paper provides conditions for the existence of a solution to the second-order nonlinear boundary value problem on the half-line of the form ∆( a(n)∆x (n)) = f (n + 1, x (n + 1)
In various physical areas, such as hydrodynamics or the unsteady flow of gas through a semi-infinite porous media, studying radially symmetric solutions leads to the Sturm–Liouville equation with boundary value conditions of the form x 0 (0) = 0, x (∞) = C, C ∈ (0, 1); see for example [1,2]
Let us remind the reader of the classical Sturm–Liouville boundary value problem on the half-line: Entropy 2021, 23, 1526. https://
Summary
Let us remind the reader of the classical Sturm–Liouville boundary value problem on the half-line: Entropy 2021, 23, 1526. In this paper we consider the following discrete boundary value problem on the half-line:. Entropy 2021, 23, 1526 a nonlinear continuous function f In both cases, with and without resonance, we prove l that ∑∞. The Przeradzki perturbation method is one of the tools used to deal with boundary value problems in the resonant case. Another classical approach is Mawhin’s coincidence degree, see for example [14]. In [19], established the sufficient conditions for the existence of one and three solutions of the following problem:. L =0 a(l ) , and in Section 3 the resonant case is presented
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