... contradiction to the definition of t0,sout ≤ βt, for any t ∈ T1,T2. 3. Proofs of main results In this section, we will deal with the proofs of main results.Proof of Theorem 1.1. From ... 1 034 of Lecture Notes in Mathematics, Springer, Berlin,Germany, 19 83. 9 M. R˚uˇziˇcka, Electrorheological Fluids: Modeling and Mathematical Theory, vol. 1748 of Lecture Notes in Mathematics, ... minr∈0,1pr, then the correspondingfunctional is coercive, if maxr∈0,1pr < minr∈0,1qr, then the corresponding functionalQihu Zhang et al. 13 From 3. 17 and the continuity of g, we...