Picone identity for quasilinear elliptic equations with p(x)p(x)-Laplacians and Sturmian comparison theory

Picone identities for quasilinear elliptic equations with p(x)p(x)-Laplacians are established, and Sturmian comparison theory is developed on the basis of Picone identities. As specializations, various elliptic equations such as linear elliptic equations, half-linear elliptic equations with p  -Laplacians, half-linear elliptic equations with p(x)p(x)-Laplacians, pseudo p-Laplacian with variable power are discussed. Generalizations are also investigated.