scholarly journals Blow-up and asymptotic behavior of solutions to a semilinear integrodifferential system

2006 ◽  
Vol 5 (3) ◽  
pp. 435-446 ◽  
Author(s):  
Qiong Chen ◽  
◽  
Chunlai Mu ◽  
Zhaoyin Xiang ◽  
Keyword(s):  
Asymptotic Behavior ◽  
Blow Up ◽  
Asymptotic Behavior Of Solutions ◽  
Integrodifferential System

BLOW-UP ANALYSIS FOR SOLUTIONS OF THE LAPLACIAN EQUATION WITH EXPONENTIAL NEUMANN BOUNDARY CONDITION IN DIMENSION TWO

2006 ◽  
Vol 08 (06) ◽  
pp. 737-761 ◽  
Author(s):  
YU-XIA GUO ◽  
JIA-QUAN LIU
Keyword(s):  
Boundary Condition ◽  
Asymptotic Behavior ◽  
Existence Theorem ◽  
Neumann Boundary Condition ◽  
Blow Up ◽  
Neumann Boundary ◽  
Asymptotic Behavior Of Solutions ◽  
Laplacian Equation ◽  
Blow Up Analysis

We consider the asymptotic behavior of solutions of the Laplacian equation with exponential Neumann boundary condition in dimension two. As an application, we prove an existence theorem of nonminimum solutions.

scholarly journals Single blow-up solutions for a slightly subcritical biharmonic equation

2006 ◽  
Vol 2006 ◽  
pp. 1-20 ◽  
Author(s):  
Khalil El Mehdi
Keyword(s):  
Boundary Condition ◽  
Asymptotic Behavior ◽  
Critical Exponent ◽  
Critical Point ◽  
Bounded Domain ◽  
Biharmonic Equation ◽  
Blow Up ◽  
Asymptotic Behavior Of Solutions ◽  
Smooth Bounded Domain ◽  
Nondegenerate Critical Point

We consider a biharmonic equation under the Navier boundary condition and with a nearly critical exponent (Pε):∆2u=u9−ε,u>0inΩandu=∆u=0on∂Ω, whereΩis a smooth bounded domain inℝ5,ε>0. We study the asymptotic behavior of solutions of (Pε) which are minimizing for the Sobolev quotient asεgoes to zero. We show that such solutions concentrate around a pointx0∈Ωasε→0, moreoverx0is a critical point of the Robin's function. Conversely, we show that for any nondegenerate critical pointx0of the Robin's function, there exist solutions of (Pε) concentrating aroundx0asε→0.

scholarly journals Blow up and asymptotic behavior of solutions for a p(x)-Laplacian equations with delay term and variadle exponents

2021 ◽  
Author(s):  
Stanilslav Antontsev ◽  
Jorge Ferreira ◽  
Erhan Pişkin ◽  
Hazal Yüksekkaya
Keyword(s):  
Asymptotic Behavior ◽  
Integral Inequality ◽  
Blow Up ◽  
Asymptotic Behavior Of Solutions ◽  
Variable Exponents ◽  
Delay Term ◽  
Laplacian Equation ◽  
Laplacian Equations ◽  
Equation With Delay ◽  
Equations With Delay

In this paper, we consider a nonlinear p .x/Laplacian equation with delay of time and variable exponents. Firstly, we prove the blow up of solutions. Then, by applying an integral inequality due to Komornik, we obtain the decay result. These results improve and extend earlier results in the literature.

Sign in / Sign up

Export Citation Format

Share Document