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Right disfocality and criteria for right disfocality of linear difference equations are considered. The criteria require the positivity of appropriate minors of a Wronskian determinant and are analogues to criteria for the disconjugacy of linear ordinary differential equations and linear difference equations. 相似文献
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Inequalities based on a generalization of concavity 总被引:4,自引:0,他引:4
Paul W. Eloe Johnny Henderson 《Proceedings of the American Mathematical Society》1997,125(7):2103-2107
The concept of concavity is generalized to functions, , satisfying order differential inequalities, , and homogeneous two-point boundary conditions, , for some . A piecewise polynomial, which bounds the function, , below, is constructed, and then is employed to obtain that , where max and denotes the supremum norm. An analogous inequality for a related Green's function is also obtained. These inequalities are useful in applications of certain cone theoretic fixed point theorems.
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Solutions are obtained for the boundary value problem, y
(n) + f(x,y) = 0, y
(i)(0) = y(1) = 0, 0 i n – 2, where f(x,y) is singular at y = 0. An application is made of a fixed point theorem for operators that are decreasing with respect to a cone. 相似文献
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Paul W. Eloe 《Proceedings of the American Mathematical Society》2003,131(5):1481-1488
We apply a method of quasilinearization to a boundary value problem for an ordinary differential equation on an unbounded domain. A uniquely determined Green's function, which is integrable and of fixed sign, is employed. The hypotheses to apply the quasilinearization method imply uniqueness of solutions. The quasilinearization method generates a bilateral iteration scheme in which the iterates converge monotonically and quadratically to the unique solution.
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Using a degree-theoretic result of Granas, a homotopy is constructed enabling us to show that if there is an a priori bound on all possible T-periodic solutions of a Volterra equation, then there is a T-periodic solution. The a priori bound is established by means of a Liapunov functional. The latter result is unusual in that no bounds on the Liapunov functional are required. Thus, in addition to the periodic solution, the equation may have both bounded and unbounded Solutions. 相似文献
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Solutions of nth order difference inequalities satisfying n boundary conditions of predetermined sign are compared to solutions of difference equalities satisfying n?1 homogenous boundary conditions. The inequalities obtained here apply to Green's functions of corresponding boundary value problems 相似文献
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Paul W. Eloe 《Journal of Mathematical Analysis and Applications》2003,287(2):444-454
This paper continues the development of disconjugacy of higher order dynamic equations on time scales. Two-point conjugate type boundary value problems for general disconjugate dynamic equations on time scales are studied and the sign properties of associated Green's functions are established. As expected, the results unify known results from the theories of ordinary differential equations and finite difference equations. 相似文献
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The Jacobi iterative method is applied to the system of linear equations arising from the discretization of the Electric Field Integral Equation (EFIE). It is shown that the resulting matrix equation is a contraction mapping, guaranteeing monotonic mean square convergence, for any initial guess, and for a preferred choice of a relaxation parameter (). Both the criterion for convergence and for the generation of the initial guess are discussed in detail. Results are shown for the 2-dimensional TM scattering by a perfectly conducting strip which illustrates the major points of this paper. The mathematical criterion herein may be applied to any electromagnetic problem employing the EFIE for perfectly conducting surfaces. 相似文献
10.
For the nth order nonlinear differential equation y
(n)(t)=f(y(t)), t [0,1], satisfying the multipoint conjugate boundary conditions, y
(j)(ai) = 0,1 i k, 0 j n
i
- 1, 0 =a
1 < a
2 < < a
k
= 1, and
i=1
k
n
i
=n, where f: [0, ) is continuous, growth condtions are imposed on f which yield the existence of at least three solutions that belong to a cone. 相似文献