共查询到20条相似文献,搜索用时 15 毫秒
1.
In this paper, we investigate a generalized discrete Green’s function that describes the general least squares solution of every second-order discrete problem with two nonlocal conditions. We develop the problem where the necessary and sufficient existence condition of ordinary discrete Green’s function is not satisfied. Some examples are also presented. 相似文献
2.
We investigate an mth-order discrete problem with additional conditions, described by m linearly independent linear functionals. We find the solution to this problem and present a formula and the existence condition of Green??s function if the general solution of a homogeneous equation is known. We obtain a relation between Green??s functions of two nonhomogeneous problems. It allows us to find Green??s function for the same equation, but with different additional conditions. The obtained results are applied to problems with nonlocal boundary conditions. 相似文献
3.
In this paper, we present an efficient numerical algorithm for solving a general class of nonlinear singular boundary value problems. This present algorithm is based on the Adomian decomposition method (ADM) and Green’s function. The method depends on constructing Green’s function before establishing the recursive scheme. In contrast to the existing recursive schemes based on ADM, the proposed numerical algorithm avoids solving a sequence of transcendental equations for the undetermined coefficients. The approximate series solution is calculated in the form of series with easily computable components. Moreover, the convergence analysis and error estimation of the proposed method is given. Furthermore, the numerical examples are included to demonstrate the accuracy, applicability, and generality of the proposed scheme. The numerical results reveal that the proposed method is very effective. 相似文献
4.
Michael I. Gil’ 《Central European Journal of Mathematics》2011,9(5):1156-1163
We consider a linear nonautonomous higher order ordinary differential equation and establish the positivity conditions and
two-sided bounds for Green’s function for the two-point boundary value problem. Applications of the obtained results to nonlinear
equations are also discussed. 相似文献
5.
In this paper, we consider the existence of positive solutions of second-order periodic boundary value problem , where 0 < ε < 1/2, g: [0, 2π] → ? is continuous, f: [0,∞) → ? is continuous and λ > 0 is a parameter.
相似文献
$$u'' + {\left( {\frac{1}{2} + \varepsilon } \right)^2}u = \lambda g\left( t \right)f\left( u \right),t \in \left[ {0,2\pi } \right],u\left( 0 \right) = u\left( {2\pi } \right),u'\left( 0 \right) = u'\left( {2\pi } \right)$$
6.
Peng-Fei Hou Jie Tong Su-Ming Xiong Jian-Feng Hu 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2013,64(5):1587-1598
Based on the two-dimensional steady-state governing equations of isotropic thermoelastic material and the compact general solution expressed in three harmonic functions, the corresponding three harmonic functions contain nine undetermined constants are constructed for a line heat source applied in the interior of a semi-infinite thermoelastic plane. All components of thermoelastic field in the semi-infinite plane can be derived by substituting the harmonic functions into the general solution. And the undetermined constants can be obtained by the compatibility conditions, equilibrium conditions and the different boundary conditions for extended Mindlin problem and extended Lorentz problem. Thus, the Green’s functions in above two cases are obtained, and the numerical results are given graphically by contours. 相似文献
7.
Yuri A. Melnikov 《Central European Journal of Mathematics》2010,8(1):53-72
Convenient for immediate computer implementation equivalents of Green’s functions are obtained for boundary-contact value
problems posed for two-dimensional Laplace and Klein-Gordon equations on some regions filled in with piecewise homogeneous
isotropic conductive materials. Dirichlet, Neumann and Robin conditions are allowed on the outer boundary of a simply-connected
region, while conditions of ideal contact are assumed on interface lines. The objective in this study is to widen the range
of effective applicability for the Green’s function version of the boundary integral equation method making the latter usable
for equations with piecewise-constant coefficients. 相似文献
8.
Jussi Behrndt 《Journal of Differential Equations》2010,249(11):2663-319
In this paper second order elliptic boundary value problems on bounded domains Ω⊂Rn with boundary conditions on ∂Ω depending nonlinearly on the spectral parameter are investigated in an operator theoretic framework. For a general class of locally meromorphic functions in the boundary condition a solution operator of the boundary value problem is constructed with the help of a linearization procedure. In the special case of rational Nevanlinna or Riesz-Herglotz functions on the boundary the solution operator is obtained in an explicit form in the product Hilbert space L2(Ω)⊕(L2m(∂Ω)), which is a natural generalization of known results on λ-linear elliptic boundary value problems and λ-rational boundary value problems for ordinary second order differential equations. 相似文献
9.
Consider Hardy’s inequalities with general weight ϕ for functions nonzero on the boundary. By an integral identity in C
1(
), define Hilbert spaces H
k
1
(Ω, ϕ) called Sobolev-Hardy spaces with weight ϕ. As a corollary of this identity, Hardy’s inequalities with weight ϕ in C
1 (
) follow. At last, by Hardy’s inequalities with weight ϕ = 1, discuss the eigenvalue problem of the Laplace-Hardy operator with critical parameter (N − 2)2/4 in H
1
1 (Ω).
相似文献
10.
D. D. Hai 《Positivity》2018,22(5):1269-1279
We prove the existence of positive solutions for the boundary value problem for certain range of the parameter \(\lambda >0\), where \(m\in (1/2,1/2+\varepsilon )\) with \(\varepsilon >0\) small, and f is superlinear or sublinear at \(\infty \) with no sign-conditions at 0 assumed.
相似文献
$$\begin{aligned} \left\{ \begin{array}{ll} y^{\prime \prime }+m^{2}y=\lambda g(t)f(y), &{}\quad 0\le t\le 2\pi , \\ y(0)=y(2\pi ), &{}\quad y^{\prime }(0)=y^{\prime }(2\pi ), \end{array} \right. \end{aligned}$$
11.
Khomsan Neamprem Thanadon Muensawat Sotiris K. Ntouyas Jessada Tariboon 《Positivity》2017,21(3):825-845
In this paper, we study the positive solutions of fractional differential system with coupled nonlocal Riemann–Liouville fractional integral boundary conditions. Our analysis relies on Leggett–Williams and Guo–Krasnoselskii’s fixed point theorems. Two examples are worked out to illustrate our main results. 相似文献
12.
Jesús Rodríguez Zachary Abernathy 《Journal of Difference Equations and Applications》2013,19(3):431-445
This paper is devoted to the study of nonlinear difference equations subject to global nonlinear boundary conditions. We provide sufficient conditions for the existence of solutions based on properties of the nonlinearities and the eigenvalues of an associated linear Sturm–Liouville problem. 相似文献
13.
Jérôme Droniou Juan-Luis Vázquez 《Calculus of Variations and Partial Differential Equations》2009,34(4):413-434
We study the existence and uniqueness of solutions of the convective–diffusive elliptic equation
posed in a bounded domain , with pure Neumann boundary conditions
Under the assumption that with p = N if N ≥ 3 (resp. p > 2 if N = 2), we prove that the problem has a solution if ∫Ω
f
dx = 0, and also that the kernel is generated by a function , unique up to a multiplicative constant, which satisfies a.e. on Ω. We also prove that the equation
has a unique solution for all ν > 0 and the map is an isomorphism of the respective spaces. The study is made in parallel with the dual problem, with equation
The dependence on the data is also examined, and we give applications to solutions of nonlinear elliptic PDE with measure
data and to parabolic problems. 相似文献
14.
In this paper, we define boundary single and double layer potentials for Laplace’s equation in certain bounded domains with
d-Ahlfors regular boundary, considerably more general than Lipschitz domains. We show that these layer potentials are invertible
as mappings between certain Besov spaces and thus obtain layer potential solutions to the regularity, Neumann, and Dirichlet
problems with boundary data in these spaces. 相似文献
15.
We investigate the existence of principal eigenvalues type problems with weights for the quasilinear operator −Δp+Vψp with mixed weighted Robin–Dirichlet boundary conditions in a bounded regular domain. We also give some results on the existence of nonprincipal eigenvalues. 相似文献
16.
Robin de Jong 《Mathematische Zeitschrift》2013,274(1-2):199-208
We give a precise formula for the value of the canonical Green’s function at a pair of Weierstrass points on a hyperelliptic Riemann surface. Further we express the ‘energy’ of the Weierstrass points in terms of a spectral invariant recently introduced by N. Kawazumi and S. Zhang. It follows that the energy is strictly larger than log 2. Our results generalize known formulas for elliptic curves. 相似文献
17.
Under study are the extremal problems of multiplicative boundary control for timeharmonic Maxwell’s equations considered with
the impedance boundary condition for the electric field. The solvability of the original extremal problem is proved. Some
sufficient conditions are derived on the original data which guarantee the stability of solutions to concrete extremal problems
with respect to certain perturbations of both the quality functional and one of the known functions that has the meaning of
the density of the electric current. 相似文献
18.
19.
We use the compact harmonic general solutions of transversely isotropic thermoelastic materials to construct the three-dimensional Green’s functions of a steady point heat source on the apex of a transversely isotropic thermoelastic cone by three newly introduced harmonic functions. All components of thermoelastic field are expressed in terms of elementary functions and are convenient to use. When the apex angle 2α equals to π, the solution reduce to the important solution of semi-infinite body with a surface point heat source. Numerical results are given graphically by contours. 相似文献