Boundary value problems for second-order partial differential equations with operator coefficients.

Fayazov, Kudratillo S.; Schock, Eberhard

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Solvability of a generalized third-order left focal problem at resonance in Banach spaces

Youwei Zhang (2013)

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This paper deals with the generalized nonlinear third-order left focal problem at resonance $\{\begin{matrix} {(p (t) u^{''} (t))}^{'} - q (t) u (t) = f (t, u (t), u^{'} (t), u^{''} (t)), t \in] t_{0}, T [, m (u (t_{0}), u^{''} (t_{0})) = 0, n (u (T), u^{'} (T)) = 0, l (u (ξ), u^{'} (ξ), u^{''} (ξ)) = 0, \end{matrix}$ where the nonlinear term is a Carathéodory function and contains explicitly the first and second-order derivatives of the unknown function. The boundary conditions that we study are quite general, involve a linearity and include, as particular cases, Sturm-Liouville boundary conditions. Under certain growth conditions on the nonlinearity, we establish the existence of the nontrivial solutions...

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On positive solutions of a class of second order nonlinear differential equations on the halfline

Svatoslav Staněk (1995)

Annales Polonici Mathematici

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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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Hartman-Wintner type criteria for half-linear second order differential equations

Zuzana Pátíková (2007)

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We establish Hartman-Wintner type criteria for the half-linear second order differential equation ${(r (t) Φ (x^{'}))}^{'} + c (t) Φ (x) = 0, Φ (x) = {| x |}^{p - 2} x, p > 1,$ where this equation is viewed as a perturbation of another equation of the same form.

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