We consider the nonlinear equation
with in and on . Where is a smooth bounded domain in , , and is a small positive parameter. We study the existence of solutions which concentrate around one or two points of . We show that this problem has no solutions that concentrate around a point of as approaches 0. In contrast to this, we construct a domain for which there exists a family of solutions which blow-up and concentrate in two different points of as approaches 0.
Submitted August 25, 2004. Published October 14, 2004.
Math Subject Classifications: 35J65, 35J40, 58E05.
Key Words: Fourth order elliptic equations; critical Sobolev exponent; blowup solution.
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| Mokhless Hammami |
Département de Mathématiques
Faculté des Sciences de Sfax
Route Soukra, 3018, Sfax, Tunisia
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