On the Cauchy problem for linear hyperbolic functional-differential equations

Alexander Lomtatidze; Jiří Šremr

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Solvability conditions of the Cauchy problem for two-dimensional systems of linear functional differential equations with monotone operators

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We establish new efficient conditions sufficient for the unique solvability of the initial value problem for two-dimensional systems of linear functional differential equations with monotone operators.

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Islam, M., Neugebauer, J.T. (2008)

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The differential equation of the form ${(q (t) k (u) {(u^{'})}^{a})}^{'} = f (t) h (u) u^{'}$ , a ∈ (0,∞), is considered and solutions u with u(0) = 0 and (u(t))² + (u’(t))² > 0 on (0,∞) are studied. Theorems about existence, uniqueness, boundedness and dependence of solutions on a parameter are given.

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Purnaras, I.K. (2006)

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Integral equations with contrasting kernels.

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Nonnegative solutions of a class of second order nonlinear differential equations

S. Staněk (1992)

Annales Polonici Mathematici

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A differential equation of the form (q(t)k(u)u')' = λf(t)h(u)u' depending on the positive parameter λ is considered and nonnegative solutions u such that u(0) = 0, u(t) > 0 for t > 0 are studied. Some theorems about the existence, uniqueness and boundedness of solutions are given.