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【期刊论文】Optimal control of some semilinear elliptic equations with critical exponent
邓引斌, Yinbin Deng, Gengsheng Wang*
Nonlinear Analysis 36(1999)915-922,-0001,():
-1年11月30日
Minimal positive solution, Optimal control
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邓引斌, Yinbin Deng*, Yi Li†
journal of differential equations 130, 179 200 (1996),-0001,():
-1年11月30日
In this paper, we consider the semilinear elliptic equation -Δu+u=u p-1+uf (x), u>0, u ∈H1(RN), N>2. (*)p For p=2N|(N-2), we show that there exists a positive constant p*>0 such that (*)p possesses at least one olution if p ∈ (0, p*) and no solutions if p>p*. Furthermore, (*)p possesses a unique solution when p=p*, and at least two solutions when p ∈ (0, p*) and 2<N<6. For N≥6, under some monotonicity onditions on f ((1.6)) we show that there exist two constants 0<p**≤ **<p* such that problem (*)p possesses a unique solution for p ∈ (0, p*), and at least two solutions if p ∈ (p**, p*).
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【期刊论文】Separation Property of Solutions for a Semilinear Elliptic Equation
邓引斌, Yi Liu, Yi Li, Yinbin Deng
Journal of Differential Equations 163, 381 406 (2000),-0001,():
-1年11月30日
In this paper, we study the following elliptic problem{Δu+k(χ)up=0 u>0 in RN in RN (V)where K(x) is a given function in C:(Rn"0) for some fixed : α∈ (0, 1), p>1 is a constant. Some existence, monotonicity and asymptotic expansion at infinity of solutions of (*) are discussed.
positive solutions, monotonicity, asymptotic expansion, elliptic equations.,
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【期刊论文】On the stability of the positive radial steady states for a semilinear Cauchy problem
邓引斌, Yinbin Denga, *, Yi Lib, Yi Liuc
Nonlinear Analysis 54(2003)291-318,-0001,():
-1年11月30日
This paper is contributed to the Cauchy problem{∂u ∂t =Δu+K({χ})up in Rn×(O,T),u(χ,0)=φ(χ) in Rn with initial function φ≠0. The stability and instability of the positive radial steady states, which are positive solutions ofΔu+K({χ})up=0, has been discussed with di3erent assumption on K(|x|) ‖‡‖λ= sup│(1+│+χ│) ‡(χ)│, where φ and ‡ are some nonnegative continuous functions in Rn, and λ is a real number.
Stability, Cauchy problem, Asymptotic stability
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【期刊论文】On the Existence of Multiple Positive Solutions for a Semilinear Problem in Exterior Domains1
邓引斌, Yinbin Deng, Yi Li
Journal of Differential Equations 181, 197-229 (2002),-0001,():
-1年11月30日
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