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Given a bounded domain Ω in R N , and a function a ∈ L q (Ω) with q > N/2, we study the existence of a positive solution for the quasilinear problemwhere g(x, s) is a Carathéodory function on Ω × (0, +∞) which may have a singularity at s = 0 and may change of sign.

In this paper we prove an existence result for a least energy nodal (or sign-changing) solution for the class of p&q problems given bywhere Ω is a smooth bounded domain in ℝ

A thorough understanding of the mixing and diffusion of turbulent jets released in a wave flow field is still lacking in the literature. This issue is undoubtedly of interest because, although stagnant ambient conditions are well known, they are almost never present in real coastal environmental problems, where the presence of waves or currents is common. As a result, jets cannot be analyzed without considering the surrounding environment, which is only rarely under stagnant conditions. The aim of the present research is to analyze from a theoretical point of view a pure jet vertically discharged in a wave motion field. Specifically, starting from the fundamental Navier–Stokes equations governing the problem joined to the continuity equation, the equations of motion and the integral equations of momentum, energy, and moment of momentum are derived. Therefore, the laws of variation of the jet length and velocity scales are deduced. Results from experiments and numerical simulations of a jet issuing in a wave environment demonstrate the validity of the proposed laws.

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