Bounds for solutions of the equation $[p(t)x^{\prime }]^{\prime }+q(t)x=h(t,x,x^{\prime })$

Miloš Ráb

Displaying similar documents to “Bounds for solutions of the equation ${[p (t) x^{'}]}^{'} + q (t) x = h (t, x, x^{'})$ ”

A note on the Cauchy problem for first order linear differential equations with a deviating argument

Robert Hakl, Alexander Lomtatidze (2002)

Archivum Mathematicum

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Conditions for the existence and uniqueness of a solution of the Cauchy problem $u^{'} (t) = p (t) u (τ (t)) + q (t), u (a) = c,$ established in [2], are formulated more precisely and refined for the special case, where the function $τ$ maps the interval $] a, b [$ into some subinterval $[τ_{0}, τ_{1}] \subseteq [a, b]$ , which can be degenerated to a point.

Optimal conditions for unique solvability of the Cauchy problem for first order linear functional differential equations

E. Bravyi, Robert Hakl, Alexander Lomtatidze (2002)

Czechoslovak Mathematical Journal

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Nonimprovable, in a sense sufficient conditions guaranteeing the unique solvability of the problem $u^{'} (t) = ℓ (u) (t) + q (t), u (a) = c,$ where $ℓ C (I, ℝ) \to L (I, ℝ)$ is a linear bounded operator, $q \in L (I, ℝ)$ , and $c \in ℝ$ , are established.

Conjugacy and disconjugacy criteria for second order linear ordinary differential equations

T. Chantladze, Alexander Lomtatidze, Douglas Ugulava (2000)

Archivum Mathematicum

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Conjugacy and disconjugacy criteria are established for the equation $u^{''} + p (t) u = 0,$ where $p :] - \infty, + \infty [\to] - \infty, + \infty [$ is a locally summable function.

On a two-point boundary value problem for second order singular equations

Alexander Lomtatidze, P. Torres (2003)

Czechoslovak Mathematical Journal

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The problem on the existence of a positive in the interval $] a, b [$ solution of the boundary value problem $u^{''} = f (t, u) + g (t, u) u^{'}; u (a +) = 0, u (b -) = 0$ is considered, where the functions $f$ and $g] a, b [\times] 0, + \infty [\to ℝ$ satisfy the local Carathéodory conditions. The possibility for the functions $f$ and $g$ to have singularities in the first argument (for $t = a$ and $t = b$ ) and in the phase variable (for $u = 0$ ) is not excluded. Sufficient and, in some cases, necessary and sufficient conditions for the solvability of that problem are established.

Displaying similar documents to “Bounds for solutions of the equation [ p ( t ) x ' ] ' + q ( t ) x = h ( t , x , x ' ) ”

A note on the Cauchy problem for first order linear differential equations with a deviating argument

Optimal conditions for unique solvability of the Cauchy problem for first order linear functional differential equations

Conjugacy and disconjugacy criteria for second order linear ordinary differential equations

On a two-point boundary value problem for second order singular equations

Displaying similar documents to “Bounds for solutions of the equation ${[p (t) x^{'}]}^{'} + q (t) x = h (t, x, x^{'})$ ”