... open ball in W of radius r2centered at 0.Proof. The proof of Proposition 3.2 is the same as the proof of the condition (A2) inthe proof of Theorem 3.1.We have proved the functional j satisfies ... Averaging of functionals of the calculus of variations and elasticity theory. Math USSR Izv. 9,33–66 (1987)10. Fan, XL, Zhao, D: The quasi-minimizer of integral functionals with m(x) growth conditions. ... technicalcondition often appears as necessary to use variational methods when we solve super-linear differential equations such as elliptic problems, Dirac equations, Hamiltonian systems, wave equations,...