A priori estimates, existence and non-existence for quasilinear cooperative elliptic systems

Abstract

Ru films were fabricated by chemical vapor deposition using Ru(C 5 H 5 ) 2 and O 2 . The deposition of Ru film was controlled by the surface reaction kinetics as the rate limiting step with activation energy of 2.48 eV below 250 • C and by the mass transport process above 250 • C. Ru films had a polycrystalline structure and showed low resistivity of about 12 µ cm. Ru films deposited at 230 • C showed excellent step coverage. We applied Ru films prepared by chemical vapor deposition to the bottom electrode of a Ba 0.25 Sr 0.75 TiO 3 capacitor and obtained good electrical characteristics.

On positive solutions of quasi-linear elliptic equations involving critical Sobolev growth

“…Under appropriate conditions on the function f , a variety of results on existence and non-existence of positive solutions have been established. This paper is a continuation of an earlier work Zou (2008) [18] of the author and, in particular, extends earlier results of Brezis and Nirenberg (1983) [3] for the semi-linear case of m = 2, and of Pucci and Serrin (1986) [12] for the quasi-linear case of m = 2.…”

“…Let λ 1 be the first eigenvalue of − m on Ω with homogeneous Dirichlet boundary data. In a recent article [18] the author studied (1.1) when f has a sub-critical growth and obtained various results on a priori estimates and existence. For simplicity, we use the following canonical prototype f (x, u, p) = λu m−1 + u p−1 + |p| q , (x,u,p) ∈ Ω × R + × R n , (1.2) where λ ∈ R, and p, q > 0 are constants, to illustrate the results.…”