Advances in Differential Equations

On the structure of positive radial solutions for quasilinear equations in annular domains

Haiyan Wang

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Abstract

We study the existence, multiplicity and nonexistence of positive radial solutions to boundary value problems for the quasilinear equation $\text{ div} \left ( A(| \nabla u|)\nabla u \right ) + \lambda h(|x|)f(u) =0$ in annular domains under general assumptions on the function $A(u)$. Various possible behaviors of the quotient $\frac{f(u)}{A(u)u}$ at zero and infinity are considered. We shall use fixed point theorems for operators on a Banach space.

Article information

Source
Adv. Differential Equations Volume 8, Number 1 (2003), 111-128.

Dates
First available in Project Euclid: 19 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355926870

Mathematical Reviews number (MathSciNet)
MR1946560

Zentralblatt MATH identifier
1042.34052

Subjects
Primary: 34B18: Positive solutions of nonlinear boundary value problems
Secondary: 35J20: Variational methods for second-order elliptic equations 35J60: Nonlinear elliptic equations 47N20: Applications to differential and integral equations

Citation

Wang, Haiyan. On the structure of positive radial solutions for quasilinear equations in annular domains. Adv. Differential Equations 8 (2003), no. 1, 111--128. https://projecteuclid.org/euclid.ade/1355926870.


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