Entire large positive radial symmetry solutions for combined quasilinear elliptic system

Authors

SESHADEV PADHI
SMITA PATI

DOI

10.3906/mat-1806-14

Abstract

We prove the existence of entire large positive solutions to the system \begin{equation*} \begin{cases} (r^{N-1}\phi_{1}(u^{\prime}))^{\prime} = r^{N-1}P_{1}(r)f(u,v),\, \, 0 \leq r < \infty \\ (r^{N-1}\phi_{2}(v^{\prime}))^{\prime} = r^{N-1}P_{2}(r)g(u,v),\, \, 0 \leq r < \infty \\ u(0) = a, \, v(0) = b, \, u^{\prime}(0) = 0, \, v^{\prime}(0) = b, \end{cases} \end{equation*} where the functions $\phi_{i}(s) = \alpha_{i}(s^{2})s, \,\, i= 1, 2$ are odd, increasing homeomorphisms, $P_{1},P_{2}:[0,\infty)\to [0,\infty)$ are continuous, and $f,g:[0,\infty) \times [0,\infty) \to [0,\infty)$ are continuous and increasing functions.

Keywords

Elliptic system, positive solutions, radial solutions, large solutions

First Page

2155

Last Page

2165

Recommended Citation

PADHI, SESHADEV and PATI, SMITA (2020) "Entire large positive radial symmetry solutions for combined quasilinear elliptic system," Turkish Journal of Mathematics: Vol. 44: No. 6, Article 14. https://doi.org/10.3906/mat-1806-14
Available at: https://journals.tubitak.gov.tr/math/vol44/iss6/14