We study the quasilinear problem $$\displaylines{ -\text{div}(h^2(u)\nabla u) + h(u)h'(u)|\nabla u|^2+u =-\lambda |u|^{q-2}u+|u|^{2 \cdot 2^*-2}u\quad \text{in } \Omega, \cr \frac{\partial u}{\partial\eta}= \mu g(x,u) \quad \text{on \partial }$$ where \(\Omega \subset \mathbb{R}^3\) is a bounded domain with regular boundary \(\partial \Omega\), \(\lambda,\mu>0\), \(1<q<4\), \(2\cdot2^{...

The condition of oligo-micelle formation of sodium di-isodecyl sulfosuccinate (SDIDS) emulsifier in hydroalcoholic solutions is used to study particle formation of vinyl chloride emulsion polymerization in a batch reactor. The change on micellization behavior was investigated by critical micelle concentration (CMC) and zeta potential parameters. To detect the occurrence of secondary nucleation ...

This paper is concerned with the existence and qualitative property of standing wave solutions ψ(t, x) = e−iEt/h̄v(x) for the nonlinear Schrödinger equation h̄ ∂ψ ∂t + h̄2 2 ψ − V (x)ψ + |ψ |p−1ψ = 0 with E being a critical frequency in the sense that minRN V (x) = E. We show that there exists a standing wave which is trapped in a neighbourhood of isolated minimum points of V and whose amplitude g...

In this study, the pitting type of corrosion growth characteristics, fatigue crack initiation and propagation behavior; axial fatigue tests were carried out on precipitation hardened martensitic Custom 450 steel in the air and 3.5wt% NaCl solution. Using the ratio of the depth to the half-width of the pits; (a/c)= 1.5±0.2 the corrosion pit depth growth law was obtained as a function of stress a...

Two different growth modes of large-area hexagonal boron nitride (h-BN) film, a conventional chemical vapor deposition (CVD) growth mode and a high-pressure CVD growth mode, were compared as a function of the precursor partial pressure. Conventional self-limited CVD growth was obtained below a critical partial pressure of the borazine precursor, whereas a thick h-BN layer (thicker than a critic...

We consider the following nonlinear elliptic equations u + u