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The proof of the Lane–Emden conjecture in four space dimensions

- P. Souplet
- Mathematics
- 1 August 2009

Abstract We partially solve a well-known conjecture about the nonexistence of positive entire solutions to elliptic systems of Lane–Emden type when the pair of exponents lies below the critical… Expand

Uniform Blow-Up Profiles and Boundary Behavior for Diffusion Equations with Nonlocal Nonlinear Source

- P. Souplet
- Mathematics
- 10 April 1999

In this paper, we introduce a new method for investigating the rate and profile of blow-up of solutions of diffusion equations with nonlocal nonlinear reaction terms. For large classes of equations,… Expand

Sharp Gradient Estimate and Yau's Liouville Theorem for the Heat Equation on Noncompact Manifolds

- P. Souplet, Q. Zhang
- Mathematics
- 3 February 2005

We derive a sharp, localized version of elliptic type gradient estimates for positive solutions (bounded or not) to the heat equation. These estimates are related to the Cheng–Yau estimate for the… Expand

Superlinear Parabolic Problems: Blow-up, Global Existence and Steady States

- P. Quittner, P. Souplet
- Mathematics
- 4 October 2007

Preliminaries.- Model Elliptic Problems.- Model Parabolic Problems.- Systems.- Equations with Gradient Terms.- Nonlocal Problems.

Liouville-type theorems and bounds of solutions of Hardy-Hénon equations

- Q. Phan, P. Souplet
- Mathematics
- 1 February 2012

Abstract We consider the Hardy–Henon equation − Δ u = | x | a u p with p > 1 and a ∈ R and we are concerned in particular with the Liouville property, i.e. the nonexistence of positive solutions in… Expand

Singularity and decay estimates in superlinear problems via Liouville-type theorems, I: Elliptic equations and systems

- P. Polácik, P. Quittner, P. Souplet
- Mathematics
- 15 September 2007

In this paper, we study some new connections between Liouville-type theorems and local properties of nonnegative solutions to superlinear elliptic problems. Namely, we develop a general method for… Expand

Blow-up in nonlocal reaction-diffusion equations

- P. Souplet
- Mathematics
- 1 November 1998

We present new blow-up results for reaction-diffusion equations with nonlocal nonlinearities. The nonlocal source terms we consider are of several types, and are relevant to various models in physics… Expand

Singularity and decay estimates in superlinear problems via liouville-type theorems. Part II: Parabolic equations

- P. Polácik, P. Quittner, P. Souplet
- Mathematics
- 6 June 2007

In this paper, we study some new connections between parabolic Liouville-type theorems and local and global properties of nonnegative classical solutions to superlinear parabolic problems, with or… Expand

Gradient blow-up for multidimensional nonlinear parabolic equations with general boundary conditions

- P. Souplet
- Mathematics
- 2002

Global solutions of inhomogeneous Hamilton-Jacobi equations

- P. Souplet, Q. Zhang
- Mathematics
- 1 December 2006

We consider the viscous Hamilton-Jacobi (VHJ) equationut-Δu=|∇u|p+h(x). For the Dirichlet problem withp>2, it is known thatgradient blow-up may occur in finite time (on the boundary). Whereas… Expand

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