共查询到20条相似文献,搜索用时 15 毫秒
1.
《Communications in Nonlinear Science & Numerical Simulation》2011,16(9):3504-3511
A boundary value method for solving a class of nonlinear singularly perturbed two point boundary value problems with a boundary layer at one end is proposed. Using singular perturbation analysis the method consists of solving two problems; namely, a reduced problem and a boundary layer correction problem. We use Pade’ approximation to obtain the solution of the latter problem and to satisfy the condition at infinity. Numerical examples will be given to illustrate the method. 相似文献
2.
We find nontrivial solutions for semilinear boundary value problems having resonance both at zero and at infinity.
Received: 14 January 1999 / Revised version: 17 May 1999 相似文献
3.
We prove existence and multiplicity theorems for nonlinear elliptic boundary value problems with noninvertible linear parts. It is considered the case in which the kernel of the linear part is unidimensional and the nonlinearity is taken either bounded or sublinear at infinity. Applications to nonlinear elasticity are given. 相似文献
4.
Thomas Krainer 《Journal of Functional Analysis》2007,244(2):351-386
We investigate general Shapiro-Lopatinsky elliptic boundary value problems on manifolds with polycylindrical ends. This is accomplished by compactifying such a manifold to a manifold with corners of in general higher codimension, and we then deal with boundary value problems for cusp differential operators. We introduce an adapted Boutet de Monvel's calculus of pseudodifferential boundary value problems, and construct parametrices for elliptic cusp operators within this calculus. Fredholm solvability and elliptic regularity up to the boundary and up to infinity for boundary value problems on manifolds with polycylindrical ends follows. 相似文献
5.
We investigate the solutions of boundary value problems of linear electroelasticity, having growth as a power function in
the neighborhood of infinity or in the neighborhood of an isolated singular point. The number of linearly independent solutions
of this type is established for homogeneous boundary value problems. 相似文献
6.
V. A. Solonnikov 《Journal of Mathematical Sciences》1983,21(5):864-868
One considers boundary and Initial-boundary value problems for Navier-Stokes equations in domains with several “outlets” at infinity. It is shown that if one prescribes the limiting values of the pressure at infinity in those “outlets” which expand sufficiently fast, then these problems are solvable in the class of vectors with a finite Dirichlet integral. 相似文献
7.
Kanishka Perera Martin Schechter 《Calculus of Variations and Partial Differential Equations》2001,12(4):359-369
We obtain nontrivial solutions for semilinear elliptic boundary value problems having asymptotic limits both at zero and
at infinity.
Received September 28, 1999 / Accepted May 9, 2000 / Published online: December 8, 2000 相似文献
8.
《Nonlinear Analysis: Theory, Methods & Applications》2004,56(5):739-750
Two results on the computation of the coincidence degree at infinity or at θ are presented. Then they are applied to the investigation of nontrivial solutions for elliptic boundary value problems in a case where the problems are resonant both at θ and at infinity. 相似文献
9.
单准周期的Riemann边值问题 总被引:1,自引:0,他引:1
本文研究了光滑封闭曲线情况下的加法与乘法单准周期Riemann边值问题,运用保角变换的方法,获得了单准周期函数的一些性质,并且对解在无穷远处作适当要求下给出了单准周期边值问题的解法. 相似文献
10.
T.S. Gadjiev N.R. SadigovaR.A. Rasulov 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(16):5566-5571
The removability of singularities of solutions for the Dirichlet problem for degenerate nonlinear elliptic equations on the boundary of a domain is studied. A method based on a priori energetic estimates of solutions to elliptic boundary value problems is used. The growth in the vicinity of a boundary point (finite or at infinity) for generalized solutions is studied. 相似文献
11.
We examine the bifurcations to positive and sign-changing solutions of degenerate elliptic equations. In the problems we study, which do not represent Fredholm operators, we show that there is a critical parameter value at which an infinity of bifurcations occur from the trivial solution. Moreover, a bifurcation occurs at each point in some unbounded interval in parameter space. We apply our results to non-monotone eigenvalue problems, degenerate semi-linear elliptic equations, boundary value differential-algebraic equations and fully non-linear elliptic equations.
12.
We study the behaviour of weak solutions (as well as their gradients) of boundary value problems for quasi-linear elliptic divergence equations in domains extending to infinity along a cone. 相似文献
13.
V. V. Shelukhin 《Journal of Applied Mathematics and Mechanics》1979,43(6):1073-1079
The boundary value problem for Burgers equations of compressible fluid is considered. Proof is given of the existence of periodic solution as the limit of solutions of initial boundary value problems in which the instant of initial data definition tends to minus infinity. 相似文献
14.
David Natroshvili 《Mathematical Methods in the Applied Sciences》1997,20(2):95-119
The three-dimensional steady state oscillation problems of the elasticity theory for homogeneous anisotropic bodies are studied. By means of the limiting absortion principle the fundamental matrices maximally decaying at infinity are constructed and the generalized Sommerfeld–Kupradze type radiation conditions are formulated. Special functional spaces are introduced in which the basic and mixed exterior boundary value problems of the steady state oscillation theory have unique solutions for arbitrary values of the oscillation parameter. Existence theorems are proved by reduction of the original boundary value problems to equivalent boundary integral (pseudodifferential) equations. © 1997 by B.G. Teubner Stuttgart-John Wiley & Sons, Ltd. 相似文献
15.
M.G. Crandall L.C. Evans R.F. Gariepy 《Calculus of Variations and Partial Differential Equations》2001,13(2):123-139
We reconsider in this paper boundary value problems for “infinity Laplacian” PDE and the relationships with optimal Lipschitz
extensions of the boundary data. fairly elegant new proofs, which clarify and simplify previous work, and may be characterized
by a comparison principle with appropriate cones. We in comparison with cones directly implies the variational principle associated
Liouville theorem for subsolutions bounded above by planes.
Received: 29 May 2000 / Accepted: 12 June 2000 / Published online: 23 April 2001 相似文献
16.
Kiyoshi Mochizuki 《Journal of Mathematical Analysis and Applications》2007,326(1):582-588
We show that the energy of solutions to the initial boundary value problem for the wave equation in exterior domains with a dissipation which is localized only near infinity tends to zero as the time goes to infinity. We do not make any geometrical condition like star-shapedness on the boundary. 相似文献
17.
In this paper, we first consider the computations of the critical groups of a functional with generalized Ahmad–Lazer–Paul type conditions both at zero and infinity. Then the abstract results are applied to investigate some new cases of the existence of nontrivial solutions of the second order Hamiltonian systems and elliptic boundary value problems, which may be resonant both at zero and infinity. 相似文献
18.
Rodica Chirila-Socolescu 《Journal of Mathematical Analysis and Applications》1977,60(2):449-460
We study the existence of a classical solution of the exterior Dirichlet problem for a class of quasilinear elliptic boundary value problems that are suggested by plane shear flow. In this connection only bounded solutions which tend to zero at infinity are of interest. A priori bounds on solutions and constructive existence proofs are given. Finally, we prove the existence of a unique bounded solution of the shear flow and we show, under certain hypotheses about the asymptotic behavior of the nonlinearity, that this solution tends to zero at infinity. As an example, we consider the case of the parabolic shear flow. 相似文献
19.
We consider a boundary value problem over a semi-infinite interval for a nonlinear autonomous system of second-order ordinary differential equations with a small parameter at the leading derivatives. We impose certain constraints on the Jacobian under which a solution to the problem exists and is unique. To transfer the boundary condition from infinity, we use the well-known approach that rests on distinguishing the variety of solutions satisfying the limit condition at infinity. To solve an auxiliary Cauchy problem, we apply expansions of a solution in the parameter. 相似文献
20.
Kazuaki Narita 《Journal of Mathematical Analysis and Applications》2011,381(2):963-965
We present an N-soliton solution of a lattice equation related to the discrete MKdV equation under an arbitrary boundary value at infinity. 相似文献