| Abstract: |
| The main goal of this lecture is analyzing the uniqueness and multiplicity of large solutions for the problem $u''=f(u)$ in $[-T,T]$ and $u(-T)=u(T)=+\infty$, where $f\in\mathcal{C}^1[0,+\infty)$ satisfies $f(0)=0$. Although this problem has been widely studied in the literature, in order to get uniqueness it is usually assumed that $f$ is increasing. In this talk, it will be shown that this condition is far from being necessary to get uniqueness. Moreover, some examples exhibiting an arbitrarily large number of large solutions will be constructed. These results are optimal for this one-dimensional problem. |
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