... equation of p-Kirchhoff type via variational methods. Bull Austral Math Soc.74, 263–277 (2006). doi:10.1017/S000497270003570X5. Perera, K, Zhang, ZT: Nontrivial solutions of Kirchhoff -type problems ... R.)Proof: By virtue of hypothes is (F5), for any given L > 0, we can find R1= R1(L )>0such thatF( x , u) ≥1pL +1pf (x, u)u,fora.e.x ∈ , |u| > R1.Thus, using hypothesis ... 2011:32http://www.boundaryvalueproblems.com/content/2011/1/32Page 5 of 8hypotheses (F0), (F1), (F2) and (1.2) are clearly satisfied.f (x, u) = arctan u +u1+u2,hypotheses (F3), (F4) and (F5) and (1.2) are clearly satisfied.3. Proofs of...