An inverse scattering problem is considered for a discontinuous Sturm-Liouville equation on the half-line [0,infinity) with a linear spectral parameter in the boundary condition. The scattering data of the problem are...
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An inverse scattering problem is considered for a discontinuous Sturm-Liouville equation on the half-line [0,infinity) with a linear spectral parameter in the boundary condition. The scattering data of the problem are defined and a new fundamental equation is derived, which is different from the classical Marchenko equation. With help of this fundamental equation, in terms of the scattering data, the potential is recovered uniquely.
The classical von Karman equations governing the boundary layer flow induced by a rotating disk are solved using the spectral homotopy analysis method and a novel successive linearisation method. The methods combine n...
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The classical von Karman equations governing the boundary layer flow induced by a rotating disk are solved using the spectral homotopy analysis method and a novel successive linearisation method. The methods combine nonperturbation techniques with the Chebyshev spectral collocation method, and this study seeks to show the accuracy and reliability of the two methods in finding solutions of nonlinear systems of equations. The rapid convergence of the methods is determined by comparing the current results with numerical results and previous results in the literature.
We consider coupled boundaryvalueproblems for second-order symmetric equation on time scales. Existence of eigenvalues of this boundaryvalue problem is proved, numbers of their eigenvalues are calculated, and their...
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We consider coupled boundaryvalueproblems for second-order symmetric equation on time scales. Existence of eigenvalues of this boundaryvalue problem is proved, numbers of their eigenvalues are calculated, and their relationships are obtained. These results not only unify equations but also contain more complicated time scales.
A discrete predator-prey system with time delay and feedback controls is studied. Sufficient conditions which guarantee the predator and the prey to be permanent are obtained. Moreover, under some suitable conditions,...
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A discrete predator-prey system with time delay and feedback controls is studied. Sufficient conditions which guarantee the predator and the prey to be permanent are obtained. Moreover, under some suitable conditions, we show that the predator species y will be driven to extinction. The results indicate that one can choose suitable controls to make the species coexistence in a long term.
We present some sufficient conditions of blowup of the solutions to Laplace equations with semilinear dynamical boundary conditions of hyperbolic type.
We present some sufficient conditions of blowup of the solutions to Laplace equations with semilinear dynamical boundary conditions of hyperbolic type.
The paper studies the singular differential equation (p(t)u ')' = p(t)f(u), which has a singularity at t = 0. Here the existence of strictly increasing solutions satisfying sup{|u(t)| : t is an element of [0,i...
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The paper studies the singular differential equation (p(t)u ')' = p(t)f(u), which has a singularity at t = 0. Here the existence of strictly increasing solutions satisfying sup{|u(t)| : t is an element of [0,infinity)} >= L > 0 is proved under the assumption that f has two zeros 0 and L and a superlinear behaviour near -infinity. The problem generalizes some models arising in hydrodynamics or in the nonlinear field theory.
An exact multiplicity result of positive solutions for the boundaryvalueproblems u '' + lambda a(t)f(u) = 0, t epsilon (0, 1), u`(0) = 0, u(1) = 0 is achieved, where lambda is a positive parameter. Here the ...
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An exact multiplicity result of positive solutions for the boundaryvalueproblems u '' + lambda a(t)f(u) = 0, t epsilon (0, 1), u`(0) = 0, u(1) = 0 is achieved, where lambda is a positive parameter. Here the function f : [0, infinity) -> [0, infinity) is C(2) and satisfies f(0) = f(s) = 0, f(u) > 0 for u epsilon (0, infinity) for some s epsilon (0, infinity). Moreover, f is asymptotically linear and f '' can change sign only once. The weight function a : [0, 1] -> (0, infinity) is C(2) and satisfies a`(t) < 0, 3(a`(t))(2) < 2a (t)a ''(t) for t epsilon [0,1]. Using bifurcation techniques, we obtain the exact number of positive solutions of the problem under consideration for lambda lying in various intervals in R. Moreover, we indicate how to extend the result to the general case.
We are concerned with the existence of positive solutions of singular second-order boundaryvalue problem u '' (t) + f(t, u (t)) = 0, t is an element of (0, 1), u(0) = u(1) = 0, which is not necessarily linear...
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We are concerned with the existence of positive solutions of singular second-order boundaryvalue problem u '' (t) + f(t, u (t)) = 0, t is an element of (0, 1), u(0) = u(1) = 0, which is not necessarily linearizable. Here, nonlinearity f is allowed to have singularities at t = 0, 1. The proof of our main result is based upon topological degree theory and global bifurcation techniques.
We study the generalized Keldys-Fichera boundaryvalue problem for a class of higher order equations with nonnegative characteristic. By using the acute angle principle and the Holder inequalities and Young inequaliti...
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We study the generalized Keldys-Fichera boundaryvalue problem for a class of higher order equations with nonnegative characteristic. By using the acute angle principle and the Holder inequalities and Young inequalities we discuss the existence of the weak solution. Then by using the inverse Holder inequalities, we obtain the regularity of the weak solution in the anisotropic Sobolev space.
We discuss the completeness of (generalized) eigenfunctions in quantum mechanics using the classical theory developed by Weyl, Titchmarsh, and Kodaira. As applications, we rigorously prove the completeness of generali...
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We discuss the completeness of (generalized) eigenfunctions in quantum mechanics using the classical theory developed by Weyl, Titchmarsh, and Kodaira. As applications, we rigorously prove the completeness of generalized eigenfunctions for the step and well potentials.
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