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fbtwitterlinkedinvimeoflicker grey 14rssslideshare1

Blow-up phenomena in semilinear elliptic partial differential equations

Title
Blow-up phenomena in semilinear elliptic partial differential equations
Funding
ARC | Discovery Projects
Contract (GA) number
DP0984807
Start Date
2009/01/01
End Date
2012/12/31
Open Access mandate
no
Organizations
-
More information
http://purl.org/au-research/grants/arc/DP0984807

 

  • New entire positive solution for the nonlinear Schrodinger equation: Coexistence of fronts and bumps

    In this paper we construct a new kind of positive solutions of $$\De u-u+u^{p}=0 \text{on} \R^2$$ when $p> 2.$ These solutions $\displaystyle{u(x,z)\sim \om(x-f(z))+ \sum_{i=1}^{\infty}\om_{0}((x, z)-\xi_i\vec{e}_{1})}$ as $L\rightarrow +\infty$ where $\om$ is a unique positive homoclinic solution of $\om"-\om+\om^{p}=0$ in $\R$ ; $\om_{0}$ is the two dimensional positive solution and $\vec{e}_{1}= (1, 0)$ and $\xi_{j}$ are points such that $\xi_{j}= jL+ \mathcal{O}(1)$ for all $j\geq 1.$ Thi...
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