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Landesman Lazer type results for first order periodic problems

Donal O'Regan (1997)

Commentationes Mathematicae Universitatis Carolinae

Existence of nonnegative solutions are established for the periodic problem y ' = f ( t , y ) a.eȯn [ 0 , T ] , y ( 0 ) = y ( T ) . Here the nonlinearity f satisfies a Landesman Lazer type condition.

Linear and nonlinear abstract differential equations of high order

Veli B. Shakhmurov (2015)

Open Mathematics

The nonlocal boundary value problems for linear and nonlinear degenerate abstract differential equations of arbitrary order are studied. The equations have the variable coefficients and small parameters in principal part. The separability properties for linear problem, sharp coercive estimates for resolvent, discreetness of spectrum and completeness of root elements of the corresponding differential operator are obtained. Moreover, optimal regularity properties for nonlinear problem is established....

Linear distributional differential equations of the second order

Milan Tvrdý (1994)

Mathematica Bohemica

The paper deals with the linear differential equation (0.1) ( p u ' ) ' + q ' u = f ' ' with distributional coefficients and solutions from the space of regulated functions. Our aim is to get the basic existence and uniqueness results for the equation (0.1) and to generalize the known results due to F. V. Atkinson [At], J. Ligeza [Li1]-[Li3], R. Pfaff ([Pf1], [Pf2]), A. B. Mingarelli [Mi] as well as the results from the paper [Pe-Tv] concerning the equation (0.1).

Local exact controllability to the trajectories of the Navier-Stokes system with nonlinear Navier-slip boundary conditions

Sergio Guerrero (2006)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper we deal with the local exact controllability of the Navier-Stokes system with nonlinear Navier-slip boundary conditions and distributed controls supported in small sets. In a first step, we prove a Carleman inequality for the linearized Navier-Stokes system, which leads to null controllability of this system at any time T>0. Then, fixed point arguments lead to the deduction of a local result concerning the exact controllability to the trajectories of the Navier-Stokes system.

Localization of nonsmooth lower and upper functions for periodic boundary value problems

Irena Rachůnková, Milan Tvrdý (2002)

Mathematica Bohemica

In this paper we present conditions ensuring the existence and localization of lower and upper functions of the periodic boundary value problem u ' ' + k u = f ( t , u ) , u ( 0 ) = u ( 2 π ) , u ' ( 0 ) = u ' ( 2 π ) , k , k 0 . These functions are constructed as solutions of some related generalized linear problems and can be nonsmooth in general.

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