Hartman-type results for p(t)-Laplacian systems Original Research Article

Consider the weighted p(t)-Laplacian ordinary system View the MathML source where f∈C([a,b]×RN,RN), w∈C([a,b],R), p∈C([a,b],R) and p(t)>1 for t∈[a,b]. It is proved that if ∃R>0 such that 〈f(t,u),u〉⩾0,∀t∈[a,b], ∀u∈RN with |u|=R, then the problem has a solution u such that |u(t)|⩽R for t∈[a,b]. As a corollary of this result, taking w(t)=tn−1, we obtain the existence of the radial solutions for the elliptic systems. Our result generalized the corresponding results obtained by Hartman and Mawhin.