Existence and Uniqueness of Positive Solutions for Semipositone Lane-Emden Equations on the Half-Axis

Imed Bachar ()
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Imed Bachar: Mathematics Department, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia

Mathematics, 2023, vol. 11, issue 19, 1-12

Abstract: Semipositone Lane–Emden type equations are considered on the half-axis. Such equations have been used in modelling several phenomena in astrophysics and mathematical physics and are often difficult to solve analytically. We provide sufficient conditions for the existence of a positive continuous solution and we describe its global behavior. Our approach is based on a perturbed operator technique and fixed point theorems. Some examples are presented to illustrate the main results.

Keywords: Lane–Emden type equations; Green’s function; positive solutions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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