Analysis and Computation of Solutions for a Class of Nonlinear SBVPs Arising in Epitaxial Growth

Amit K Verma, Biswajit Pandit and Ravi P. Agarwal
Additional contact information
Amit K Verma: Department of Mathematics, Indian Institute of Technology Patna, Patna 801106, Bihar, India
Biswajit Pandit: Department of Mathematics, Indian Institute of Technology Patna, Patna 801106, Bihar, India
Ravi P. Agarwal: Department of Mathematics, Texas A & M University-Kingsville, 700 University Blvd., MSC 172, Kingsville, TX 78363-8202, USA

Mathematics, 2021, vol. 9, issue 7, 1-25

Abstract: In this work, the existence and nonexistence of stationary radial solutions to the elliptic partial differential equation arising in the molecular beam epitaxy are studied. Since we are interested in radial solutions, we focus on the fourth-order singular ordinary differential equation. It is non-self adjoint, it does not have exact solutions, and it admits multiple solutions. Here, ? ? R measures the intensity of the flux and G is stationary flux. The solution depends on the size of the parameter ? . We use a monotone iterative technique and integral equations along with upper and lower solutions to prove that solutions exist. We establish the qualitative properties of the solutions and provide bounds for the values of the parameter ? , which help us to separate existence from nonexistence. These results complement some existing results in the literature. To verify the analytical results, we also propose a new computational iterative technique and use it to verify the bounds on ? and the dependence of solutions for these computed bounds on ? .

Keywords: radial solutions; SBVPs; non-self-adjoint operator; Green’s function; lower solution; upper solution; iterative numerical approximations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/9/7/774/pdf (application/pdf)
https://www.mdpi.com/2227-7390/9/7/774/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:9:y:2021:i:7:p:774-:d:529159

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().