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Zbl 0973.35077
Cuesta, Mabel; Takáč, Peter
A strong comparison principle for positive solutions of degenerate elliptic equations.
(English)
[J] Differ. Integral Equ. 13, No.4-6, 721-746 (2000). ISSN 0893-4983

The authors present a strong comparison principle for the following class of quasilinear elliptic boundary-value problems $$\cases -\text{div}(a(x,\nabla u))- b(x,u)= f(x)\quad\text{in }\Omega\\ u|_{\partial\Omega}= 0.\endcases\tag 1$$ More precisely, they investigate the validity of the strong comparison principle for nonnegative weak solutions $u\in W^{1,p}_0(\Omega)$ to (1).
[Messoud Efendiev (Berlin)]
MSC 2000:
*35J65 (Nonlinear) BVP for (non)linear elliptic equations
35B05 General behavior of solutions of PDE
34B15 Nonlinear boundary value problems of ODE
34C11 Qualitative theory of solutions of ODE: Growth, etc.
35J60 Nonlinear elliptic equations
35J70 Elliptic equations of degenerate type

Keywords: strong comparison principle; weak solutions; quasilinear elliptic BVP

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