共查询到20条相似文献,搜索用时 15 毫秒
1.
Of concern is a class of abstract semilinear integrodifferential equations with nonlocal initial conditions. Under some suitable hypotheses, we establish some new theorems about the existence of asymptotically almost automorphic solutions to the integrodifferential equations. Moreover, an example is given to illustrate our results. 相似文献
2.
We study local and global existence of solutions for some semilinear parabolic initial boundary value problems with autonomous nonlinearities having a “Newtonian” nonlocal term. 相似文献
3.
Zhihua Dong 《Applicable analysis》2018,97(5):825-841
This paper deals with a parabolic system with different diffusion coefficients and coupled nonlocal sources, subject to homogeneous Dirichlet boundary conditions. The conditions on global existence, simultaneous or non-simultaneous blow-up, blow-up set, uniform blow-up profiles and boundary layer are got using comparison principle and asymptotic analysis methods. 相似文献
4.
Alexander Gladkov Tatiana Kavitova 《Mathematical Methods in the Applied Sciences》2020,43(8):5464-5479
We prove the global existence and blow-up of solutions of an initial boundary value problem for nonlinear nonlocal parabolic equation with nonlinear nonlocal boundary condition. Obtained results depend on the behavior of variable coefficients for large values of time. 相似文献
5.
Using fixed point techniques, we study the existence and multiplicity of positive radial solutions for two classes of nonlocal elliptic systems defined on bounded annular domains or exterior domains. To this end, we reduce our problem to second-order functional ordinary elliptic systems. Our approach also allows us to study systems involving various orders, which serve as models for the suspension bridge equations. 相似文献
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The aim of this paper is to investigate the existence, uniqueness, and asymptotic behavior of solutions for a coupled system of quasilinear parabolic equations under nonlinear boundary conditions, including a system of quasilinear parabolic and ordinary differential equations. Also investigated is the existence of positive maximal and minimal solutions of the corresponding quasilinear elliptic system as well as the uniqueness of a positive steady-state solution. The elliptic operators in both systems are allowed to be degenerate in the sense that the density-dependent diffusion coefficients Di(ui) may have the property Di(0)=0 for some or all i. Our approach to the problem is by the method of upper and lower solutions and its associated monotone iterations. It is shown that the time-dependent solution converges to the maximal solution for one class of initial functions and it converges to the minimal solution for another class of initial functions; and if the maximal and minimal solutions coincide then the steady-state solution is unique and the time-dependent solution converges to the unique solution. Applications of these results are given to three model problems, including a porous medium type of problem, a heat-transfer problem, and a two-component competition model in ecology. These applications illustrate some very interesting distinctive behavior of the time-dependent solutions between density-independent and density-dependent diffusions. 相似文献
8.
Yu. T. Sil’chenko 《Journal of Mathematical Sciences》2008,149(6):1701-1707
For a linear parabolic equation with the principal part in divergence form, a boundary-value problem with nonlocal (irregular)
conditions of integral type is considered. Sufficient conditions of the unique solvability are found for the above-mentioned
problem.
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Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions),
Vol. 17, Differential and Functional Differential Equations. Part 3, 2006. 相似文献
9.
Zhanbing Bai 《Applied mathematics and computation》2010,215(12):4191-3640
By the use of the Krasnosel’skii’s fixed point theorem, the existence of one or two positive solutions for the nonlocal fourth-order boundary value problem
10.
Hernán R. Henríquez Verónica Poblete Juan C. Pozo 《Journal of Mathematical Analysis and Applications》2014
In this paper we establish the existence of mild solutions for a non-autonomous abstract semi-linear second order differential equation submitted to nonlocal initial conditions. Our approach relies on the existence of an evolution operator for the corresponding linear equation and the properties of the Hausdorff measure of non-compactness. 相似文献
11.
Ioan I. Vrabie 《Journal of Evolution Equations》2013,13(3):693-714
We consider the nonlinear delay differential evolution equation $$\left\{\begin{array}{ll} u'(t) \in Au(t) + f(t, u_t), \quad \quad t \in \mathbb{R}_+,\\ u(t) = g(u)(t),\qquad \qquad \quad t \in [-\tau, 0], \end{array} \right.$$ u ′ ( t ) ∈ A u ( t ) + f ( t , u t ) , t ∈ R + , u ( t ) = g ( u ) ( t ) , t ∈ [ - τ , 0 ] , where τ ≥ 0, X is a real Banach space, A is the infinitesimal generator of a nonlinear semigroup of contractions whose Lipschitz seminorm decays exponentially as ${t \mapsto {\rm{e}}^{-\omega t}}$ t ? e - ω t when ${t \to + \infty}$ t → + ∞ and ${f : {\mathbb{R}}_+ \times C([-\tau, 0]; \overline{D(A)}) \to X}$ f : R + × C ( [ - τ , 0 ] ; D ( A ) ¯ ) → X is jointly continuous. We prove that if f Lipschitz with respect to its second argument and its Lipschitz constant ? satisfies the condition ${\ell{\rm{e}}^{\omega\tau} < \omega, g : C_b([-\tau, +\infty); \overline{D(A)}) \to C([-\tau, 0]; \overline{D(A)})}$ ? e ω τ < ω , g : C b ( [ - τ , + ∞ ) ; D ( A ) ¯ ) → C ( [ - τ , 0 ] ; D ( A ) ¯ ) is nonexpansive and (I – A)?1 is compact, then the unique C 0-solution of the problem above is almost periodic. 相似文献
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This paper deals with a nonlinear degenerate parabolic system with nonlocal source and nonlocal boundaries. By super-solution, sub-solution and auxiliary functions, a criteria for nonnegative solution of global existence and blow-up in finite time is obtained for this degenerate nonlocal problem. Finally, the blow-up rates of blow-up solutions are also estimated. 相似文献
14.
Positive solutions of higher-order nonlinear fractional differential systems with nonlocal boundary conditions 下载免费PDF全文
The paper deals with the existence and multiplicity of positive solutions for a system of higher-order nonlinear fractional differential equations with nonlocal boundary conditions. The main tool
used in the proof is fixed point index theory in cone. Some limit type conditions for ensuring the existence of positive solutions are given. 相似文献
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We establish conditions for the existence and nonexistence of global solutions of an initial–boundary value problem for a system of semilinear parabolic equations with nonlinear nonlocal boundary conditions. The results depend on the behavior of variable coefficients as t→∞. 相似文献
17.
K. Munusamy C. Ravichandran Kottakkaran Sooppy Nisar Behzad Ghanbari 《Mathematical Methods in the Applied Sciences》2020,43(17):10319-10331
In this paper, we discuss the existence of mild solution of functional integrodifferential equation with nonlocal conditions. To establish this results by using the resolvent operator theory and Sadovskii-Krasnosel'skii type of fixed point theorem and to show the usefulness and the applicability of our results to a broad class of functional integrodifferential equations, an example is given to illustrate the theory. 相似文献
18.
Global existence and blow-up solutions for doubly degenerate parabolic system with nonlocal source 总被引:1,自引:0,他引:1
Jian Wang 《Journal of Mathematical Analysis and Applications》2011,374(1):290-310
This paper deals with the following nonlocal doubly degenerate parabolic system
19.
A strongly coupled elliptic system under the homogeneous Dirichlet boundary condition denoting the steady-state system of
the Lotka-Volterra two-species competitive system with cross-diffusion effects is considered. By using the implicit function
theorem and the Lyapunov-Schmidt reduction method, the existence of the positive solutions bifurcating from the trivial solution
is obtained. Furthermore, the stability of the bifurcating positive solutions is also investigated by analyzing the associated
characteristic equation. 相似文献
20.
Youpeng Chen 《Applicable analysis》2013,92(7):1495-1510
In this article, we investigate the positive solution of a localized quasilinear parabolic system with nonlocal boundary conditions. Under certain conditions, the global existence and finite time blow-up criteria are established, and the global blow-up behaviour is also obtained. 相似文献