Harnack type inequality and a priori estimates for solutions of a class of semilinear elliptic equations

For dimensions 3 n 6, we derive here the Harnack type inequality for C2, positive solutions u of in ball B(0,3R) in where R 1. Here μ>0 and the constant C=C(n,μ,K, K). For dimension 3, we assume that K is Hölder continuous with exponent θ with . While for dimensions n=4,5,6, assume that K C1 is bounded between two positive constants and that in a neighborhood of a critical point x0 of K, we havecx−x0θ−1 K(x) Cx−x0θ−1 for c, C>0 and . As an application, a priori estimates for solutions are obtained in star shaped domains