共查询到20条相似文献,搜索用时 15 毫秒
1.
Albo Carlos Cavalheiro 《Applications of Mathematics》2006,51(6):619-628
In the paper we study the equation L
u
= f, where L is a degenerate elliptic operator, with Neumann boundary condition in a bounded open set μ. We prove existence and uniqueness
of solutions in the space H(μ) for the Neumann problem. 相似文献
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Norimichi Hirano 《Journal of Mathematical Analysis and Applications》2006,314(1):210-218
The multiplicity of solutions for semilinear elliptic equations with exponential growth nonlinearities is treated. The approach to the problem is a variational method. 相似文献
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亚纯函数系数高阶复域微分方程解的不动点 总被引:2,自引:0,他引:2
研究了一类亚纯函数系数的高阶线性微分方程的解的不动点问题,应用值分布的理论和方法,得到了复域微分方程亚纯解的不动点性质. 相似文献
8.
Zhi-ting Xu 《应用数学学报(英文版)》2009,25(2):291-304
Using general means, we establish several new Philos-type oscillation theorems for the second order damped elliptic differential equation
Σi,j=1 N Di[aij(x)Djy]+Σi=1 N bi(x)Diy+c(x)f(y)=0
under quite general assumptions. The obtained results are extensions of the well-known oscillation results due to Kamenev, Philos, Yan for second order linear ordinary differential equations and improve recent results of Xu, Jia and Ma. 相似文献
Σi,j=1 N Di[aij(x)Djy]+Σi=1 N bi(x)Diy+c(x)f(y)=0
under quite general assumptions. The obtained results are extensions of the well-known oscillation results due to Kamenev, Philos, Yan for second order linear ordinary differential equations and improve recent results of Xu, Jia and Ma. 相似文献
9.
Guochun Wen 《分析论及其应用》2005,21(2):118-131
The present paper deals with the mixed boundary value problem for elliptic equations with degenerate rank 0. We first give the formulation of the problem and estimates of solutions of the problem, and then prove the existence of solutions of the above problem for elliptic equations by the above estimates and the method of parameter extension. We use the complex method, namely first discuss the corresponding problem for degenerate elliptic complex equations of first order, afterwards discuss the above problem for degenerate elliptic equations of second order. 相似文献
10.
A. Ya. Sahakyan 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2008,43(2):100-103
The present paper considers the Dirichlet problem for properly elliptic equations of fourth order in the exterior of an ellipse. No restrictions on the multiplicities of the roots of the characteristic polynomial are assumed. 相似文献
11.
Zhi Ting Xu 《数学学报(英文版)》2010,26(11):2165-2178
We obtain some new Kamenev-type oscillation theorems for the second order semilinear elliptic differential equation with damping N ∑i,j=1Di[aij(x)Djy]+N∑i=1bi(x)Diy+c(x)f(y)=0 under quite general assumptions. These results are extensions of the recent results of Sun [Sun, Y. G.: New Kamenev-type oscillation criteria of second order nonlinear differential equations with damping. J. Math. Anal. Appl., 291, 341-351 (2004)] in a natural way. In particular, we do not impose any additional conditions on the damped functions bi (x) except the continuity. Several examples are given to illustrate the main results. 相似文献
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We study the wellposedness in the Gevrey classes Gs and in C∞ of the Cauchy problem for weakly hyperbolic equations of higher order. In this paper we shall give a new approach to the case that the characteristic roots oscillate rapidly and vanish at an infinite number of points. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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Gabriele Bonanno Giuseppina D'Aguì 《Journal of Mathematical Analysis and Applications》2009,358(2):223-637
The aim of this paper is to establish the existence of an unbounded sequence of weak solutions to a Neumann problem for elliptic equations involving the p-Laplacian. 相似文献
14.
Massimo Grossi 《Proceedings of the American Mathematical Society》2000,128(6):1665-1672
We prove that the least-energy solution of the problem
where is a ball, and if , if , is unique (up to rotation) if is small enough.
15.
Lijun Pan 《Journal of Mathematical Analysis and Applications》2008,343(2):904-918
By using the coincidence degree theory of Mawhin, we study the existence of periodic solutions for higher order differential equations with deviating argument . Some new results on the existence of periodic solutions of the equations are obtained. Meanwhile, an example is given to illustrate our results. 相似文献
16.
Jan Chabrowski 《Ricerche di matematica》2007,56(2):297-319
We consider the semilinear Neumann problem involving the critical Sobolev exponent with an indefinite weight function and
a concave purturbation. We prove the existence of two distinct solutions.
相似文献
17.
Guo Chun Wen 《数学学报(英文版)》2013,29(12):2233-2244
In this article, we first transform the general uniformly elliptic systems of first order equations with certain conditions into the complex equations, and propose the discontinuous Riemann- Hilbert problem and its modified well-posedness for the complex equations. Then we give a priori estimates of solutions of the modified discontinuous Riemann-Hilbert problem for the complex equations and verify its solvability. Finally the solvability results of the original discontinuous Riemann-Hilbert boundary value problem can be derived. The discontinuous boundary value problem possesses many applications in mechanics and physics etc. 相似文献
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In this paper, we estimate the number of subnormal solutions for higher order linear periodic differential equations, and
estimate the growth of subnormal solutions and all other solutions. We also give a representation of subnormal solutions of
a class of higher order linear periodic differential equations. 相似文献
20.
In this paper, we develop a new discontinuous Galerkin (DG) finite element method for solving time dependent partial differential equations (PDEs) with higher order spatial derivatives. Unlike the traditional local discontinuous Galerkin (LDG) method, the method in this paper can be applied without introducing any auxiliary variables or rewriting the original equation into a larger system. Stability is ensured by a careful choice of interface numerical fluxes. The method can be designed for quite general nonlinear PDEs and we prove stability and give error estimates for a few representative classes of PDEs up to fifth order. Numerical examples show that our scheme attains the optimal -th order of accuracy when using piecewise -th degree polynomials, under the condition that is greater than or equal to the order of the equation.