PERIODIC BOUNDARY VALUE PROBLEMS FOR nTH-ORDER ORDINARY DIFFERENTIAL EQUATIONS WITH p-LAPLACIAN
نویسنده
چکیده
We prove existence results for solutions of periodic boundary value problems concerning the nth-order differential equation with p-Laplacian [φ(x(n−1)(t))]′ = f (t,x(t),x′(t), . . . , x(n−1)(t)) and the boundary value conditions x(i)(0)=x(i)(T), i= 0, . . . ,n− 1. Our method is based upon the coincidence degree theory of Mawhin. It is interesting that f may be a polynomial and the degree of some variables among x0,x1, . . . ,xn−1 in the function f (t,x0,x1, . . . ,xn−1) is allowed to be greater than 1.
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