Displaying similar documents to “Boundary value problems for second-order partial differential equations with operator coefficients.”

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

Youwei Zhang (2013)

Mathematica Bohemica

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This paper deals with the generalized nonlinear third-order left focal problem at resonance ( p ( t ) u ' ' ( t ) ) ' - q ( t ) u ( t ) = f ( t , u ( t ) , u ' ( t ) , u ' ' ( t ) ) , t ∈ ] 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 , 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...

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

Zuzana Pátíková (2007)

Mathematica Bohemica

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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.