Abstract:We prove an abstract result of existence of "good" generalized subsolutions for convex operators. Its application to semilinear elliptic equations leads to an extension of results by P.B-M.Pierre concerning a criterion for the existence of solutions to a semilinear elliptic or parabolic equation with a convex nonlinearity. We apply this result to the model problem −∆u = a|∇u| p + b|u| q + f with Dirichlet boundary conditions where a, b > 0, p, q > 1. No other condition is made on p and q.
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