Asymptotic behavior and existence results for a biharmonic equation involving the critical Sobolev exponent in a five-dimensional domain
2010
In this paper, we consider the problem $(Q_\varepsilon)$ : $\Delta ^2 u=
u^9 +\varepsilon f(x)$ in $\Omega$, $u=\Delta u=0$ on $\partial\Omega$,
where $\Omega$ is a bounded and smooth domain in $R^5$, $\varepsilon$ is a
small positive parameter, and $f$ is a smooth function. Our main
purpose is to characterize the solutions with some assumptions on
the energy. We prove that these solutions blow up at a critical
point of a function depending on $f$ and the regular part of the
Green's function. Moreover, we construct families of solutions of
$(Q_\varepsilon)$ which satisfy the conclusions of the first part.
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