scholarly journals Uniqueness and asymptotic behavior of solutions with boundary blow-up for a class of nonlinear elliptic equations

1997 ◽  
Vol 14 (2) ◽  
pp. 237-274 ◽  
Author(s):  
M. Marcus ◽  
L. Véron
Keyword(s):  
Asymptotic Behavior ◽  
Elliptic Equations ◽  
Blow Up ◽  
Nonlinear Elliptic Equations ◽  
Asymptotic Behavior Of Solutions ◽  
Nonlinear Elliptic

Multiple boundary blow-up solutions for nonlinear elliptic equations

2003 ◽  
Vol 133 (2) ◽  
pp. 225-235 ◽  
Author(s):  
Amandine Aftalion ◽  
Manuel del Pino ◽  
René Letelier
Keyword(s):  
Elliptic Equations ◽  
Blow Up ◽  
A Priori ◽  
Nonlinear Elliptic Equations ◽  
Positive Parameter ◽  
Number Of Solutions ◽  
Bounded Smooth Domain ◽  
Nonlinear Elliptic ◽  
Bounded Smooth

We consider the problem Δu = λf(u) in Ω, u(x) tends to +∞ as x approaches ∂Ω. Here, Ω is a bounded smooth domain in RN, N ≥ 1 and λ is a positive parameter. In this paper, we are interested in analysing the role of the sign changes of the function f in the number of solutions of this problem. As a consequence of our main result, we find that if Ω is star-shaped and f behaves like f(u) = u(u−a)(u−1) with ½ < a < 1, then there is a solution bigger than 1 for all λ and there exists λ0 > 0 such that, for λ < λ0, there is no positive solution that crosses 1 and, for λ > λ0, at least two solutions that cross 1. The proof is based on a priori estimates, the construction of barriers and topological-degree arguments.

Estimates for Blow-Up Solutions to Nonlinear Elliptic Equations with p-Growth in the Gradient

2010 ◽  
pp. 219-234 ◽  
Author(s):  
Vincenzo Ferone ◽  
Ester Giarrusso ◽  
Basilio Messano ◽  
Maria Rosaria Posteraro
Keyword(s):  
Elliptic Equations ◽  
Blow Up ◽  
Nonlinear Elliptic Equations ◽  
Nonlinear Elliptic

On the Existence of Positive Decaying Entire Solutions for a Class of Sublinear Elliptic Equations

1988 ◽  
Vol 40 (5) ◽  
pp. 1156-1173 ◽  
Author(s):  
Yasuhiro Furusho ◽  
Takaŝi Kusano
Keyword(s):  
Asymptotic Behavior ◽  
Elliptic Equations ◽  
Early Stage ◽  
Nonlinear Elliptic Equations ◽  
Entire Solution ◽  
Entire Solutions ◽  
Nonlinear Elliptic ◽  
The Subject ◽  
Image Position ◽  
Simple Equations

In recent years there has been a growing interest in the existence and asymptotic behavior of entire solutions for second order nonlinear elliptic equations. By an entire solution we mean a solution of the elliptic equation under consideration which is guaranteed to exist in the whole Euclidean N-space RN, N ≧ 2. For standard results on the subject the reader is referred to the papers [2-7, 9-21].The study of entire solutions, which at an early stage was restricted to simple equations of the form Δu + f(x, u) = 0, x ∊ RN, Δ being the N-dimensional Laplacian, has now been extended and generalized to elliptic equations of the typeAwhere

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