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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).

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