Displaying similar documents to “Superconvergence of a finite element method for linear integro-differential problems.”

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...

On local motion of a compressible barotropic viscous fluid bounded by a free surface

W. Zajączkowski (1992)

Banach Center Publications

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We consider the motion of a viscous compressible barotropic fluid in ℝ³ bounded by a free surface which is under constant exterior pressure, both with surface tension and without it. In the first case we prove local existence of solutions in anisotropic Hilbert spaces with noninteger derivatives. In the case without surface tension the anisotropic Sobolev spaces with integration exponent p > 3 are used to omit the coefficients which are increasing functions of 1/T, where T is the...