## Communications in Mathematical Analysis

### Oscillation Criteria For Bounded Solutions For Some Nonlinear Diffusion Equations Via Picone-Type Formulae

#### Abstract

By means of Picone's type identities and inequalities some comparison results for problems related to the equation $$\nabla .\{ A(u) \nabla u \} + c(x)u + f(u) = g(x) \text{ in } \mathbb R^n$$ are established.Because of its principal part,this type of equation finds its applications in various physical phenomena like in nonlinear diffusion problems,flows through porous media, plasma physics,...etc. In this paper we show how versatile can the use of Picone-type formulae be for these type of quasilinear equations. Our main focus is to establish some oscillation criteria for classical non trivial and bounded solutions of some of these types of equations.We will display here some criteria conditions for some model equations.The ultimate aim is that by means of comparison methods and some Picone-type formulae,this could lead to getting the oscillation criteria of some more general equations.

#### Article information

Source
Commun. Math. Anal., Volume 12, Number 2 (2012), 1-10.

Dates
First available in Project Euclid: 16 March 2012

https://projecteuclid.org/euclid.cma/1331929867

Mathematical Reviews number (MathSciNet)
MR2905127

Zentralblatt MATH identifier
1266.35071

Subjects
Primary: 35J60: Nonlinear elliptic equations
Secondary: 35J70: Degenerate elliptic equations 34C10

#### Citation

Tadie. Oscillation Criteria For Bounded Solutions For Some Nonlinear Diffusion Equations Via Picone-Type Formulae. Commun. Math. Anal. 12 (2012), no. 2, 1--10. https://projecteuclid.org/euclid.cma/1331929867