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- Title
A Study on Solutions for a Class of Higher-Order System of Singular Boundary Value Problem.
- Authors
Pandit, Biswajit; Verma, Amit K.; Agarwal, Ravi P.
- Abstract
In this article, we propose a fourth-order non-self-adjoint system of singular boundary value problems (SBVPs), which arise in the theory of epitaxial growth by considering hte equation 1 r β r β 1 r β (r β Θ ′) ′ ′ ′ = 1 2 r β K 11 μ ′ Θ ′ 2 + 2 μ Θ ′ Θ ″ + K 12 μ ′ φ ′ 2 + 2 μ φ ′ φ ″ + λ 1 G 1 (r) , 1 r β r β 1 r β (r β φ ′) ′ ′ ′ = 1 2 r β K 21 μ ′ Θ ′ 2 + 2 μ Θ ′ Θ ″ + K 22 μ ′ φ ′ 2 + 2 μ φ ′ φ ″ + λ 2 G 2 (r) , where λ 1 ≥ 0 and λ 2 ≥ 0 are two parameters, μ = p r 2 β − 2 , p ∈ R + , G 1 , G 2 ∈ L 1 [ 0 , 1 ] such that M 1 * ≥ G 1 (r) ≥ M 1 > 0 , M 2 * ≥ G 2 (r) ≥ M 2 > 0 and K 12 > 0 , K 11 ≥ 0 , and K 21 > 0 , K 22 ≥ 0 are constants that are connected by the relation (K 12 + K 22) ≥ (K 11 + K 21) and β > 1 . To study the governing equation, we consider three different types of homogeneous boundary conditions. We use the transformation t = r 1 + β 1 + β to deduce the second-order singular boundary value problem. Also, for β = p = G 1 (r) = G 2 (r) = 1 , it admits dual solutions. We show the existence of at least one solution in continuous space. We derive a sign of solutions. Furthermore, we compute the approximate bound of the parameters to point out the region of nonexistence. We also conclude bounds are symmetric with respect to two different transformations.
- Subjects
BOUNDARY value problems; EPITAXY
- Publication
Symmetry (20738994), 2023, Vol 15, Issue 9, p1729
- ISSN
2073-8994
- Publication type
Article
- DOI
10.3390/sym15091729