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Wavelet characterization of Sobolev spaces with variable exponent

100%

Izuki M.

tom 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).

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

100%

Matzakos N. , Papageorgiou N.

tom 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.