共查询到20条相似文献,搜索用时 15 毫秒
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Tomasz Ma?olepszy Wojciech Okrasiñski 《Journal of Mathematical Analysis and Applications》2010,366(1):372-384
The problem of the estimating of a blow-up time for solutions of Volterra nonlinear integral equation with convolution kernel is studied. New estimates, lower and upper, are found and, moreover, the procedure for the improvement of the lower estimate is presented. Main results are illustrated by examples. The new estimates are also compared with some earlier ones related to a shear band model. 相似文献
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The interest in the use of quasimodes, or almost frequencies and almost eigenfunctions, to describe asymptotics for low‐frequency and high‐frequency vibrations in certain singularly perturbed spectral problems, which depend on a small parameter ε, has been recently highlighted in many papers. In this paper we deal with the low frequencies for a Steklov‐type eigenvalue homogenization problem: we consider harmonic functions in a bounded domain of ?2, and strongly alternating boundary conditions of the Dirichlet and Steklov type on a part of the boundary. The spectral parameter appears in the boundary condition on small segments Tε of size O(ε) periodically distributed along the boundary; ε also measures the periodicity of the structure. We consider associated second‐order evolution problems on spaces of traces that depend on ε, and we provide estimates for the time t in which standing waves, constructed from quasimodes, approach their solutions uε(t) as ε→0. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
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Sufficient conditions are given so that bounded and unbounded solutions of the Volterra integral equation are oscillatory or nonoscillatory. Asymptotic behaviour of such solutions is also studied. 相似文献
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Igor Chudinovich Christian Constanda Eduardo Aguilera Gmez 《Mathematical Methods in the Applied Sciences》2004,27(7):769-780
The existence, uniqueness, stability, and integral representation of distributional solutions are investigated for the equations of motion of a thin elastic plate with a combination of displacement and moment‐stress components prescribed on the boundary. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
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Received September 7,1995 相似文献
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研究一类带有R-S积分边值条件的非线性分数阶朗之万方程边值问题.利用Leray-Schauder非线性抉择和Leray-Schauder度理论,得到几个新的存在性结果.最后给出一个例子来证明主要结论的应用性. 相似文献
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研究一类带记忆边界条件波动系统解的长时间性态.在初边值满足一定条件时,利用Faedo-Galerkin近似方法得到了系统解的存在唯一性.使用扰动能量方法,证明了系统解的一致衰减性. 相似文献
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Positive solutions for nonlinear Caputo fractional differential equations with integral boundary conditions 总被引:1,自引:0,他引:1
Wengui Yang 《Journal of Applied Mathematics and Computing》2014,44(1-2):39-59
In this paper, we consider the properties of Green’s function for a class of nonlinear Caputo fractional differential equations with integral boundary conditions by constructing an available integral operator. By means of well-known fixed point theorems and lower and upper solutions method, some new existence and nonexistence criteria of single or multiple positive solutions for fractional differential equation boundary value problems are established. As applications, some interesting examples are presented to illustrate the main results. 相似文献
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The existence of a unique solution to Maxwell's equations defined in an exterior domain with impedance boundary condition is established for all frequencies. This is accomplished by reducing this problem to that of solving a system of singular integral equations and then regularizing this system such that the Riesz theory is applicable. We also consider the inverse problem in which it is desired to determine the impedance from a knowledge of the far field pattern. By restricting the impedance to lie a priori in a compact set results are obtained on the existence, uniqueness, and stability of the solution to this inverse scattering problem. 相似文献
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《Communications in Nonlinear Science & Numerical Simulation》2011,16(1):101-111
This paper is concerned with a class of second order impulsive differential equations with integral boundary conditions. Under different combinations of superlineary and sublinearity of nonlinear term and the impulses, various existence, multiplicity, and nonexistence results for positive solutions are derived in terms of the parameter lies in some intervals. The results obtained herein generalize and improve some known results. 相似文献
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This paper is devoted to studying initial-boundary value problems for semilinear wave equations and derivative semilinear wave equations with variable coefficients on exterior domain with subcritical exponents in n space dimensions. We will establish blow-up results for the initial-boundary value problems. It is proved that there can be no global solutions no matter how small the initial data are, and also we give the life span estimate of solutions for the problems. 相似文献
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We investigate quantitative properties of nonnegative solutions \(u(x)\ge 0\) to the semilinear diffusion equation \(\mathcal {L}u= f(u)\), posed in a bounded domain \(\Omega \subset \mathbb {R}^N\) with appropriate homogeneous Dirichlet or outer boundary conditions. The operator \(\mathcal {L}\) may belong to a quite general class of linear operators that include the standard Laplacian, the two most common definitions of the fractional Laplacian \((-\Delta )^s\) (\(0<s<1\)) in a bounded domain with zero Dirichlet conditions, and a number of other nonlocal versions. The nonlinearity f is increasing and looks like a power function \(f(u)\sim u^p\), with \(p\le 1\). The aim of this paper is to show sharp quantitative boundary estimates based on a new iteration process. We also prove that, in the interior, solutions are Hölder continuous and even classical (when the operator allows for it). In addition, we get Hölder continuity up to the boundary. Particularly interesting is the behaviour of solution when the number \(\frac{2s}{1-p}\) goes below the exponent \(\gamma \in (0,1]\) corresponding to the Hölder regularity of the first eigenfunction \(\mathcal {L}\Phi _1=\lambda _1 \Phi _1\). Indeed a change of boundary regularity happens in the different regimes \(\frac{2s}{1-p} \gtreqqless \gamma \), and in particular a logarithmic correction appears in the “critical” case \(\frac{2s}{1-p} = \gamma \). For instance, in the case of the spectral fractional Laplacian, this surprising boundary behaviour appears in the range \(0<s\le (1-p)/2\). 相似文献
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M. P. Vishnevskiî 《Siberian Mathematical Journal》1993,34(5):801-811
Novosibirsk. Translated fromSibirskiî Matematicheskiî Zhurnal, Vol. 34, No. 5, pp. 11–22, September–October, 1993. 相似文献
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The existence of positive solutions for a class of fractional equations involving the Riemann–Liouville fractional derivative with integral boundary conditions is investigated. By means of the monotone iteration method and some inequalities associated with the Green function, we obtain the existence of a positive solution and establish the iterative sequence for approximating the solution. 相似文献
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Existence of positive solutions for singular impulsive differential equations with integral boundary conditions
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In this paper, we study the existence of positive solutions for singular impulsive differential equations with integral boundary conditions where the nonlinearity f(t,u,v) may be singular at u = 0 and v = 0. The proof is based on the theory of Leray–Schauder degree, together with a truncation technique. Some recent results in the literature are generalized and improved. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
19.
Chen Zhimin 《Arkiv f?r Matematik》1990,28(1-2):371-381
A sharp result on global small solutions to the Cauchy problem $$u_t = \Delta u + f\left( {u,Du,D^2 u,u_t } \right)\left( {t > 0} \right),u\left( 0 \right) = u_0 $$ In Rn is obtained under the the assumption thatf is C1+r forr>2/n and ‖u 0‖C2(R n ) +‖u 0‖W 1 2 (R n ) is small. This implies that the assumption thatf is smooth and ‖u 0 ‖W 1 k (R n )+‖u 0‖W 2 k (R n ) is small fork large enough, made in earlier work, is unnecessary. 相似文献