[PDF] Top 20 On the uniqueness of singular solutions to boundary initial value problems in linear elastodynamics

... Working within the framework of the linearized dynamical theory of thermoelasticity, Dafermos [9 J established the existence, uniqueness and asymptotic stability of "generalized solution[r] ... See full document

... the singular BVPs of the form ()- ...for singular BVPs via various ...with singular boundary value problems, for example, Legendre polynomials [], Chebyshev polynomials [], ... See full document

... be singular, distributional and impulsive. Dif- ferential equations, initial and boundary conditions and impulses may depend function- ally on the unknown function and/or on its derivatives, and may ... See full document

... exact solutions by the classical techniques such as trigonometry, calculus ...these solutions one can know the behavior of differential equation under the given different ...equations. Singular ... See full document

... As a result, our nonlinearity f ( k , u ) may be singular at u = 0 and may change sign. Remark 1.1. Recall a map f : N × (0, ∞ ) → R is continuous if it is continuous as a map of the topological space N × (0, ∞ ) ... See full document

... nonlinear boundary value ...lower solutions [] manifests itself as an effective and flexible mechanism that offers theoretical as well as constructive existence results in a closed set, generated by ... See full document

... where a min{0, inf{τ t : 0 ≤ t ≤ 1}}, b max{1, sup{τt : 0 ≤ t ≤ 1}}, and the existence of positive solutions to 1.1 is obtained. When τt t − r in 1.1, Agarwal and O’Regan in 5, Lin and Xu in 6 discussed the ... See full document

... the initial boundary value problem for the linear homogeneous ...existence, uniqueness and regularity of solutions to an initial boundary value problem for ... See full document

... Note that this problem was considered in 6 where the authors proved the existence of one positive solution for 1.1 by using Krasnoselskii’s fixed point theorem and nonlinear alternative of Leray-Schauder type in a cone ... See full document

... the initial data of a generalized solution to the problem ...and uniqueness of weak solutions to a class of nonlinear beam equation are established under certain assumptions (locally Lipschitz plus ... See full document

... Motivated by above works, under various appropriate assumptions on p , q and K t ( ) , we will obtain the existence and uniqueness of positive solution of problem (1.1) for λ in different circumstances. In our ... See full document

... the uniqueness results of this section is the role of continuous dependence of solutions on boundary ...of solutions on initial ...of uniqueness properties on solutions ... See full document

... the uniqueness of solutions for singular higher- order continuous boundary value problems by using mixed monotone method, for example, see 6, 14, ...the uniqueness of ... See full document

... and uniqueness of smooth positive solutions to a class of singular m-point boundary value problems of second-order ordinary differential ...and uniqueness of smooth ... See full document

... of boundary value problems for certain Hamiltonian systems and some estimates for their ...everywhere uniqueness of absolute minimizers in the corresponding problem of calculus of variations ... See full document

... 1. Diethelm, K, Freed, AD: On the solutions of nonlinear fractional order differential equations used in the modelling of viscoplasticity. In: Keil F, Mackens W, Voss H, Werthers J (eds.) Scientific Computing in ... See full document

... Lidstone problems. We show that the solvability of these problems is reduced to the existence of a fixed point of an operator ...of solutions to auxiliary problems are also investigated ...the ... See full document

... Singular nonlinear boundary value problems for higher order ordinary differential equations, Nonlin.. Singular boundary value problems, Bull.[r] ... See full document

... a boundary value problem can have only the trivial solution; this is a ...Therefore, solutions of the boundary value problem ... See full document

... Suppose that ϕ(u) = u – φ(u) and ϕ : [, + ∞ ) → [, + ∞ ) is continuous, nondecreasing, positive in (, + ∞ ) and ϕ() = . Thus, for u ≥ v, d(Tu, Tv) ≤ d(u, v) – ϕ(d(u, v)). Finally, take into account that for the zero ... See full document