共查询到20条相似文献,搜索用时 0 毫秒
1.
Yoshikazu Kobayashi Toshitaka Matsumoto Naoki Tanaka 《Journal of Mathematical Analysis and Applications》2007,330(2):1042-1067
In this paper we introduce the notion of semigroups of locally Lipschitz operators which provide us with mild solutions to the Cauchy problem for semilinear evolution equations, and characterize such semigroups of locally Lipschitz operators. This notion of the semigroups is derived from the well-posedness concept of the initial-boundary value problem for differential equations whose solution operators are not quasi-contractive even in a local sense but locally Lipschitz continuous with respect to their initial data. The result obtained is applied to the initial-boundary value problem for the complex Ginzburg–Landau equation. 相似文献
2.
Yuqing Chen 《Journal of Mathematical Analysis and Applications》2006,315(1):337-348
In this paper, we study the existence problem of anti-periodic solutions for the following first order evolution equation:
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This paper is devoted to the study of positive solutions of the semilinear elliptic equation Δu+K(|x|)u−p=0, x∈Rn with n?3 and p>0. Asymptotic behaviours of sky states and uniqueness of singular sky states are obtained via invariant manifold theory of dynamical systems. The Dirichlet problem in exterior domains is also studied. It is proved that this problem has infinitely many positive solutions with fast growth. 相似文献
4.
Qing Liu 《Journal of Mathematical Analysis and Applications》2011,377(1):110-120
In this paper we study the existence of anti-periodic mild solutions for a class of semilinear evolution equations in Banach spaces and extend some related results in this direction. An example is given to illustrate our results. 相似文献
5.
Junhong Ha Shin-ichi Nakagiri Hiroki Tanabe 《Journal of Mathematical Analysis and Applications》2008,346(2):374-383
In this paper we establish the strong Fréchet differentiability of maps from the set of initial values and forcing terms into the set of solutions for semilinear second order evolution equations. Also, under the weaker conditions of nonlinear terms we establish the strong Gâteaux differentiability of the solution maps. An application of results to semilinear strongly damped wave equations is given. 相似文献
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Kai Liu 《Stochastic Processes and their Applications》1997,70(2):219-241
Sufficient conditions for almost surely asymptotic stability with a certain decay function of sample paths, which are given by mild solutions to a class of semilinear stochastic evolution equations, are presented. The analysis is based on introducing approximating system with strong solution and using a limiting argument to pass on some properties of strong solution to our purposes. Several examples are studied to illustrate our theory. In particular, by means of the derived results we lose conditions of certain stochastic evolution systems from Haussmann (1978) to obtain the pathwise stability for mild solution with probability one. 相似文献
8.
Ryôhei Kakizawa 《Journal of Mathematical Analysis and Applications》2011,378(2):375-386
We are concerned with the determination of the asymptotic behavior of strong solutions to the initial-boundary value problem for general semilinear parabolic equations by the asymptotic behavior of these strong solutions on a finite set. More precisely, if the asymptotic behavior of the strong solution is known on a suitable finite set which is called determining nodes, then the asymptotic behavior of the strong solution itself is entirely determined. We prove the above property by the energy method. 相似文献
9.
P. Cannarsa G. Fragnelli J. Vancostenoble 《Journal of Mathematical Analysis and Applications》2006,320(2):804-818
In this paper we study controllability properties of semilinear degenerate parabolic equations. Due to degeneracy, classical null controllability results do not hold in general. Thus we investigate results of ‘regional null controllability’, showing that we can drive the solution to rest at time T on a subset of the space domain, contained in the set where the equation is nondegenerate. 相似文献
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In this paper, we use new analyses to assert that there are three positive solutions of Eq. (1.1) in infinite cylinder domain with hole . 相似文献
12.
Jiqin Deng 《Journal of Mathematical Analysis and Applications》2007,336(2):1395-1405
In this paper, by using the fixed point theory, under quite general conditions on the nonlinear term, we obtain an existence result of bounded positive solutions of semilinear elliptic equations in exterior domain of Rn, n?3. 相似文献
13.
The existence of self-similar and asymptotically self-similar solutions of the nonlinear wave equation with or in R
3×R
+ for small Cauchy data is proven if . A counterexample is given which shows that the lower bound on α is sharp.
Received April 1999 – Accepted September 1999 相似文献
14.
In this article some noncoercive semilinear equations are investigated. Here, a subset of a right side for which the corresponding boundary value problems are uniquely solvable is described. 相似文献
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Yoshikazu Giga 《Journal of Mathematical Analysis and Applications》2006,316(2):538-555
A nonnegative blowing up solution of the semilinear heat equation ut=Δu+up with p>1 is considered when initial data u0 satisfies
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We prove an existence and uniqueness result for almost‐periodic solutions to the quasilinear evolution equations (1) and (5). Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
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In this paper, applying the theory of semigroups of operators to evolution family and Banach fixed point theorem, we prove the existence and uniqueness of an (a) almost automorphic (weighted pseudo almost automorphic) mild solution of the semilinear evolution equation x′(t)=A(t)x(t)+f(t,x(t)) in Banach space under conditions. 相似文献
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