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Wavelet characterization of Sobolev spaces with variable exponent

Izuki M.

Journal of Applied Analysis

2011

Vol. 17, nr 1

37-49

Our aim is to get characterizations and unconditional bases of variable Sobolev spaces Lp (·),s(Rn) in terms of wavelets. As an application, we obtain the sampling theorem in Lp (·),s(Rn).

On a nonlinear Kirchhoff-Carrier wave equation in the unit membrane: the quadratic convergence and asymptotic expansion of solutions

Long N., Ngoc L.

Demonstratio Mathematica

2007

Vol. 40, nr 2

365-392

In this paper we consider the initial-boundary value problem for the nonlinear wave equation.

Existence of periodic solutions for quasilinear ordinary differential eqasilinear ordinary diefferential equations with discontinuities

Matzakos N., Papageorgiou N.

Demonstratio Mathematica

2000

Vol. 33, nr 4

753-770

We consider a quasilinear differential equation with discontinuous right hand side and periodic boundary conditions. To obtain an existence theory we pass to a relevant multivalued variant of the original problem, which we solve. Our approach is a mixture of the variational method (for nonsmooth locally Lipschitz functionals) and of the method of upper and Iower solutions. The mixing of these two techniques is made possible by a nonresonance condition below the first nonzero eigenvalue of the one-dimensional p-Laplacian with periodic boundary conditions.