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A strong comparison principle for positive solutions of degenerate elliptic equations. (English) Zbl 0973.35077
The authors present a strong comparison principle for the following class of quasilinear elliptic boundary-value problems $\begin{cases} -\text{div}(a(x,\nabla u))- b(x,u)= f(x)\quad\text{in }\Omega\\ u|_{\partial\Omega}= 0.\end{cases}\tag{1}$ More precisely, they investigate the validity of the strong comparison principle for nonnegative weak solutions $$u\in W^{1,p}_0(\Omega)$$ to (1).

##### MSC:
 35J65 Nonlinear boundary value problems for linear elliptic equations 35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs 34B15 Nonlinear boundary value problems for ordinary differential equations 34C11 Growth and boundedness of solutions to ordinary differential equations 35J60 Nonlinear elliptic equations 35J70 Degenerate elliptic equations