Language:
EN
| Published:
23-07-2022
|
Abstract
| pp. 93-109
The functional differential equation (g(x'(t)))' = (Fx)(t) is considered. Here g is an increasing homomorphism on ℝ, g(0) = 0 and F: C1(J)→L1(J) is a continuous operator satisfying a growth condition with respect to x. A class of nonlinear functional boundary conditions is considered and sufficient conditions for the existence at least one positive and one negative solutions of the boundary value problems are given. Results are proved by the homotopy theory, the Leray-Schauder degree and the Borsuk theorem.
Language:
EN
| Published:
30-09-1993
|
Abstract
| pp. 89-98
The paper establishes sufficient conditions for the existence of solutions of a one-parameter differential equation x" = f(t,x,x',λ) satisfying some of the following boundary conditions: γ(x) = 0, x'(a) = x'(b) = 0, x'(a) = x'(b) = 0, x(c)-x(d) = 0 and x'(a) = x'(t0) = x'(b) = 0. Here γ is a functional. The application is given for a class of one-parameter functional boundary value problems.
Roman Badora
,
Barbara Przebieracz
,
Peter Volkmann
Language:
EN
| Published:
30-09-2010
|
Abstract
| pp. 7-13
A stability result for the Pexider equation will be derived from a stability theorem published in [9] for the Cauchy functional equation. Then we discuss the quality of some constants occuring in this context; as a model case we consider functions defined on the multiplicative semigroup {1, 0}.
Language:
EN
| Published:
30-09-1996
|
Abstract
| pp. 111-125
Sufficient conditions for the existence of solutions of one-parameter functional boundary value problems of the type x" = f(t,x,xt,x',x't,λ), (x0,x'0) ∈ {(ϕ,χ+c); c∈R}, α(x|J) = A, β(x(T)-x|J) = B are given. Here f: J×R×Cr×R×Cr×R→R is continuous, ϕ,χ∈Cr, α,β are continuous increasing functionals, A,B∈R and x|J is the restriction of x to J=[0,T]. Results are proved by the Leray-Schauder degree method.
English