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Zbl 1089.35019
Jaroš, Jaroslav; Takaŝi, Kusano; Yoshida, Norio
Picone-type inequalities for half-linear elliptic equations and their applications. (English)
[J] Adv. Math. Sci. Appl. 12, No. 2, 709-724 (2002). ISSN 1343-4373

Picone-type inequalities for some degenerate quasilinear elliptic operators are established and Sturmian comparison theorems are derived as applications extending previous work by the authors [J. Inequal. Appl. 6, No. 4, 387--404 (2001; Zbl 1088.35024)]. The equations considered are of the form $L[v]=f(x)$ and $\tilde L[v]=0$, where $$L[v]=\text{div } (A(x)|\nabla v|^{\alpha-1} \nabla v)+C(x)|v|^{\beta-1}v$$ and $$\tilde L[v]=\text{div }(A(x)|\nabla v|^{\alpha-1}\nabla v)+C(x)|v|^{\beta-1}v+D(x)|v|^{\gamma-1}v.$$ The functions $A(x)$, $C(x)$, $D(x)$ are defined and positive in some bounded piecewise smooth domain $G\subset \Bbb R^n$, and $0<\gamma<\alpha<\beta$. Moreover, $A\in C^1(\overline{G})$, $C,D,f\in C(\overline{G})$. Oscillation results are also obtained by using Sturmian comparison theorems.
[Ruxandra Stavre (Bucureşti)]

MSC 2000:: *35J60 Nonlinear elliptic equations
35B45 A priori estimates

Keywords: Picone inequality; Sturmian comparison theorem; degenerate quasilinear elliptic operator

Citations: Zbl 1088.35024

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