On the Cauchy problem for linear hyperbolic functional-differential equations
نویسندگان
چکیده
منابع مشابه
On the Darboux problem for linear hyperbolic functional-differential equations
Theorems on the Fredholm alternative and well-posedness of the Darboux problem ∂2u(t, x) ∂t ∂x = `(u)(t, x) + q(t, x), u(t, x0) = φ(t) for t ∈ [a, b], u(t0, x) = ψ(x) for x ∈ [c, d] are established, where ` : C(D;R) → L(D;R) is a linear bounded operator, q ∈ L(D;R), t0 ∈ [a, b], x0 ∈ [c, d], φ : [a, b]→ R, ψ : [c, d]→ R are absolutely continuous functions, and D = [a, b] × [c, d]. New sufficien...
متن کاملOscillatory Solutions of the Cauchy Problem for Linear Differential Equations
We consider the Cauchy problem for second and third order linear differential equations with constant complex coefficients. We describe necessary and sufficient conditions on the data for the existence of oscillatory solutions. It is known that in the case of real coefficients the oscillatory behavior of solutions does not depend on initial values, but we show that this is no longer true in the...
متن کاملOn the Cauchy Singular Problem for Systems of Functional Differential Equations
satisfies the condition f ρ ∈ Lloc(]a, b]; R). In regular case where f ρ ∈ L([a, b]; R) for any ρ > 0, problem (1), (2) is investigated in detail (see, e.g., [1]–[4], [9], [10] and the references therein). We are, in the main, interested in the case when f ρ is nonintegrable on [a, b], having singularity at t = a. In this case, the problem (1), (2) is singular one. The methods of investigation ...
متن کاملNew Optimal Conditions for Unique Solvability of the Cauchy Problem for First Order Linear Functional Differential Equations
The nonimprovable sufficient conditions for the unique solvability of the problem u ′(t) = `(u)(t) + q(t), u(a) = c, where ` : C(I; ) → L(I; ) is a linear bounded operator, q ∈ L(I; ), c ∈ , are established which are different from the previous results. More precisely, they are interesting especially in the case where the operator ` is not of Volterra’s type with respect to the point a.
متن کاملOn a singular Cauchy problem for functional differential equations with non-increasing non-linearities∗
We obtain general conditions sufficient for the solvability of a singular Cauchy problem for functional differential equations with non-increasing non-linearities. 1 Problem setting and introduction The aim of this note is to establish some general conditions sufficient for the existence of a solution of a singular Cauchy problem for a class of non-linear functional differential equations. More...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Czechoslovak Mathematical Journal
سال: 2012
ISSN: 0011-4642,1572-9141
DOI: 10.1007/s10587-012-0037-2