共查询到20条相似文献,搜索用时 78 毫秒
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Jie Xiao 《Journal of Differential Equations》2006,224(2):277-295
Let u(t,x) be the solution of the heat equation (∂t-Δx)u(t,x)=0 on subject to u(0,x)=f(x) on Rn. The main goal of this paper is to characterize such a nonnegative measure μ on that f(x)?u(t2,x) induces a bounded embedding from the Sobolev space , p∈[1,n) into the Lebesgue space , q∈(0,∞). 相似文献
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Liangping Jiang 《Journal of Mathematical Analysis and Applications》2007,326(2):1379-1382
The classical criterion of asymptotic stability of the zero solution of equations x′=f(t,x) is that there exists a function V(t,x), a(‖x‖)?V(t,x)?b(‖x‖) for some a,b∈K, such that for some c∈K. In this paper we prove that if f(t,x) is bounded, is uniformly continuous and bounded, then the condition that can be weakened and replaced by and contains no complete trajectory of , t∈[−T,T], where , uniformly for (t,x)∈[−T,T]×BH. 相似文献
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An implicit iteration process for nonexpansive semigroups 总被引:1,自引:0,他引:1
Duong Viet Thong 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(17):6116-6120
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In this article we classify all positive finite energy solutions of the equation in Rn where and a point x∈Rn is denoted as x=(y,z)∈Rk×Rn-k. As a consequence we obtain the best constant and extremals of a related Hardy-Sobolev inequality. 相似文献
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