[کتاب][B] Nonlinear PDEs: Mathematical models in biology, chemistry and population genetics

M Ghergu, V Radulescu - 2011‏ - books.google.com
The emphasis throughout the present volume is on the practical application of theoretical
mathematical models hel** to unravel the underlying mechanisms involved in processes …

On a long-standing conjecture of E. De Giorgi: symmetry in 3D for general nonlinearities and a local minimality property

G Alberti, L Ambrosio, X Cabré - Acta Applicandae Mathematica, 2001‏ - Springer
This paper studies a conjecture made by De Giorgi in 1978 concerning the one-dimensional
character (or symmetry) of bounded, monotone in one direction, solutions of semilinear …

One-dimensional symmetry of bounded entire solutions of some elliptic equations

H Berestycki, F Hamel, R Monneau - 2000‏ - projecteuclid.org
For the 1-dimensional problem, we refer to [5],[11],[19], or [23]. For the low dimensions case
n= 2, 3 (assuming also that f is C1), the same result had been obtained by Ghoussoub and …

Back to the Keller-Osserman condition for boundary blow-up solutions

S Dumont, L Dupaigne, O Goubet… - Advanced Nonlinear …, 2007‏ - degruyter.com
This article is concerned with the existence, uniqueness and numerical approximation of
boundary blow up solutions for elliptic PDE's Δu= f (u), where f satisfies the so-called Keller …

On positive solutions of semilinear elliptic equations

EN Dancer, K Schmitt - Proceedings of the American Mathematical Society, 1987‏ - ams.org
This paper is concerned with necessary conditions for the existence of positive solutions of
the semilinear problem $\Delta u+ f (u)= 0, x\in\Omega, u= 0, x\in\partial\Omega $, whose …

Stable and finite Morse index solutions on 𝐑ⁿ or on bounded domains with small diffusion

E Dancer - Transactions of the American Mathematical Society, 2005‏ - ams.org
In this paper, we study bounded solutions of $-\Delta u= f (u) $ on $\mathbf {R}^ n $(where $
n= 2$ and sometimes $ n= 3$) and show that, for most $ f $'s, the weakly stable and finite …

Infinitely many solutions of a quasilinear elliptic problem with an oscillatory potential

P Omari, F Zanolin - Communications in Partial Differential …, 1996‏ - Taylor & Francis
Infinitely many solutions of a quasilinear elliptic problem with an oscillatory potential<xref ref-type='fn'
rid=' Page 1 COMMUN. IN PARTIAL DIFFERENTIAL EQUATIONS, 21(5&6), 721-733 (1996) …

On the existence of a maximal weak solution for a semilinear elliptic equation

EN Dancer, G Sweers - 1989‏ - projecteuclid.org
(0.1) where n is a bounded domain in IRn and f: n X IR-+ IR. It is well known, see eg [16], that
for f E C1 (!'2 x IR) and hence solutions in C2+19 (! 1), there is a solution in between a …

[PDF][PDF] Towards a counter-example to a conjecture of De Giorgi in high dimensions

D Jerison, R Monneau - Annali di Matematica Pura ed Applicata, 2004‏ - Citeseer
In this paper we consider entire solutions to semilinear elliptic equations. We show that
solutions that are monotone in one direction are energy minimizers and we discuss …

Existence results for classes of sublinear semipositone problems

A Castro, JB Garner, R Shivaji - Results in Mathematics, 1993‏ - Springer
We consider the semipositone problem-Δ u (x)= λ f (u (x))\\;\\\x ∈ Ω\cr\qquad\qquad\qquad u
(x)= 0\\;\\x ∈ ∂ Ω\cr where λ> 0 is a constant, Ω is a bounded region in R n with a smooth …