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In this paper we prove a sharp global existence theorem in all dimensions for nonlinear wave equations with power-type nonlinearities. The proof is based on a weighted Strichartz estimate involving powers of the Lorentz distance.

Objectives: The study was aimed to evaluate the oxidative/nitrosative stress status in prostate cancer (CaP) and benign prostatic hyperplasia (BPH). Design and methods: 312 men from two different populations were included: 163 men from Macedonia (73 CaP patients, 67 BPH patients and 23 control subjects) and 149 men from Turkey (34 prostate cancer patients, 100 BPH patients and 15 control subjects). We measured erythrocyte malondialdehyde (MDA) levels, erythrocyte activities of superoxide dismutase (CuZn-SOD), glutathione peroxidase (GPX) and catalase (CAT); plasma nitrite/nitrate (NO 2 − /NO 3 − ), cGMP and 8-hydroxy-2′-deoxyguanosine (8-OHdG) levels.Results: A similar pattern of alteration in the oxidative/nitrosative stress-related parameters was found in both, Macedonian and Turkish studied samples: higher MDA concentrations with lower GPX and CuZn-SOD activities in CaP patients versus controls and BPH groups. The CAT activity was decreased in the CaP patients versus controls in the Turkish studied sample. Furthermore, CaP patients had increased plasma NO 2 − /NO 3 − and cGMP levels versus controls and BPH groups in both studied samples.Conclusions: This study has confirmed an imbalance in the oxidative stress/antioxidant status and revealed an altered nitrosative status in prostate cancer patients.

The Maxwell-Dirac system describes the interaction of an electron with its own electromagnetic field. We prove the existence of soliton-like solutions of Maxwell-Dirac in (3+l)-Minkowski space-time. The solutions obtained are regular, stationary in time, and localized in space. They are found by a variational method, as critical points of an energy functional. This functional is strongly indefinite and presents a lack of compactness. We also find soliton-like solutions for the Klein-Gordon-Dirac system, arising in the Yukawa model.