HIGHER FRACTIONAL ORDER p-LAPLACIAN BOUNDARY VALUE PROBLEM AT RESONANCE ON AN UNBOUNDED DOMAIN

In this work, we use the Ge and Ren extension of Mawhin's coincidence degree theory to investigate the solvability of the p-Laplacian fractional order boundary value problem of the form (phi(p)(D(0+)(alpha)x(t)))' = f(t, x(t), D(0+)(alpha-3)x(t), D(0+)(alpha-2)x(t), D(0+)(alpha)(-1)x(t), D(0+)(alpha)x(t)), t is an element of (0, + infinity) x(0) = 0 = D(0+)(alpha-3)x(0), D(0+)(alpha-2)x(0) = integral(1 )(0)D(0+)(alpha-2)x(t)dA(t), lim(t ->+infinity) D(0+)(alpha)(-1)x(t) = Sigma(m)(i=1) (sic)(i)D(0+)(alpha)(-1)x(xi(i)), D(0+)(alpha)(-1)x(infinity) = 0, where 3 < alpha <= 4. The conditions integral(1)(0) dA(t) = 1, integral(1)(0) tdA(t) = 0, Sigma(m)(i=1) (sic)(i )and Sigma(m)(i=1) (sic)(i)xi(-1)(i) = 0 are critical for resonance.