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Asymptotics of positive solutions for a biharmonic equation involving critical exponent. (English) Zbl 0977.35043

Summary: The semilinear biharmonic problem \[ \left\{\begin{aligned} \Delta^2u & = c_0u^{p-\varepsilon},\quad \text{in }\Omega\\ u & >0,\quad \text{in }\Omega\\ u=& \Delta u = 0,\quad \text{on }\partial\Omega.\end{aligned}\right. \] involving critical growth is considered for \(\varepsilon\to 0^+\) on a bounded convex domain. Rather complete results are obtained for the asymptotic behavior of positive solutions. The similar problem for the Laplacian was studied by Han, Rey, and other authors.

MSC:

35J40 Boundary value problems for higher-order elliptic equations
35B45 A priori estimates in context of PDEs
35J60 Nonlinear elliptic equations
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