Advances in Differential Equations

On the solutions of quasilinear elliptic equations with a polynomial-type reaction term

Alberto Ferrero

Full-text: Open access

Abstract

We study existence and boundedness of solutions for the quasilinear elliptic equation $-\Delta_{m} u=\lambda(1+u)^p$ in a bounded domain $\Omega$ with homogeneous Dirichlet boundary conditions. The assumptions on both the parameters $\lambda$ and $p$ are fundamental. Strange critical exponents appear when boundedness of solutions is concerned. In our proofs we use techniques from calculus of variations, from critical-point theory, and from the theory of ordinary differential equations.

Article information

Source
Adv. Differential Equations, Volume 9, Number 11-12 (2004), 1201-1234.

Dates
First available in Project Euclid: 18 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355867901

Mathematical Reviews number (MathSciNet)
MR2099555

Zentralblatt MATH identifier
05054506

Subjects
Primary: 35J60: Nonlinear elliptic equations
Secondary: 35B33: Critical exponents 35J70: Degenerate elliptic equations 47J30: Variational methods [See also 58Exx]

Citation

Ferrero, Alberto. On the solutions of quasilinear elliptic equations with a polynomial-type reaction term. Adv. Differential Equations 9 (2004), no. 11-12, 1201--1234. https://projecteuclid.org/euclid.ade/1355867901


Export citation