Bifurcation Problem for Biharmonic Asymptotically Linear Elliptic Equations
Publish place: Theory of Approximation and Applications، Vol: 11، Issue: 1
Publish Year: 1396
نوع سند: مقاله ژورنالی
زبان: English
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شناسه ملی سند علمی:
JR_MSJI-11-1_002
تاریخ نمایه سازی: 26 مرداد 1402
Abstract:
In this paper, we investigate the existence of positive solutions for the ellipticequation \Delta^{۲}\,u+c(x)u = \lambda f(u) on a bounded smooth domain \Omega of \R^{n}, n\geq۲, with Navier boundary conditions. We show that there exists an extremal parameter\lambda^{\ast}>۰ such that for \lambda< \lambda^{\ast}, the above problem has a regular solution butfor \lambda> \lambda^{\ast}, the problem has no solution even in the week sense.We also show that \lambda^{\ast}=\frac{\lambda_{۱}}{a} if \lim_{t\rightarrow \infty}f(t)-at=l\geq۰ and for \lambda< \lambda^{\ast}, the solution is unique but for l<۰ and \frac{\lambda_{۱}}{a}<\lambda< \lambda^{\ast}, the problem has two branches of solutions, where \lambda_{۱} is the first eigenvalue associated to the problem.
Authors
Makkia Dammak
University of Tunis El Manar, Higher Institute of Medical Technologies of Tunis ۰۹ doctor Zouhair Essafi Street ۱۰۰۶ Tunis,Tunisia
Majdi El Ghord
University of Tunis El Manar, Faculty of Sciences of Tunis, Campus Universities ۲۰۹۲ Tunis, Tunisia