# Existence and asymptotic behavior of nontrivial solutions to the Swift-Hohenberg equation

@article{Marino2016ExistenceAA, title={Existence and asymptotic behavior of nontrivial solutions to the Swift-Hohenberg equation}, author={Greta Marino and Sunra Mosconi}, journal={arXiv: Classical Analysis and ODEs}, year={2016} }

In this paper, we discuss several results regarding existence, non-existence and asymptotic properties of solutions to $u""+qu"+f(u)=0$, under various hypotheses on the parameter $q$ and on the potential $F(t)=\int_0^tf(s)\, ds$, generally assumed to be bounded from below. We prove a non-existence result in the case $q\le 0$ and an existence result of periodic solution for: 1) almost every suitably small (depending on $F$), positive values of $q$; 2) all suitably large (depending on $F$) values…

## One Citation

Existence and asymptotic properties of solutions for a nonlinear Schrödinger elliptic equation from geophysical fluid flows

- Computer Science, MathematicsAppl. Math. Lett.
- 2019

The existence theorem and asymptotic properties of radial positive solutions are established by using a new renormalization technique.

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