Radial and asymptotically constant solutions for nonautonomous elliptic equations

ABSTRACT

We consider semilinear elliptic equations of the form $\mathrm{\Delta }u+g(|x|,u)=0$ on ${\mathbb{R}}^N$. Given a suitable positive z satisfying $g(r,z)=0,\mathrm{\forall }r\in {\mathbb{R}}^{+}$, we discuss the existence of positive radial solutions u with $u\left(\mathrm{\infty }\right)=z$.

Keywords:

• Semilinear elliptic equations
• asymptotic behavior

AMS Classifications:

• 35J61
• 35B40

Acknowledgments

This project has been funded with support from the Lebanese University.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This project has been funded with support from the Lebanese University.