Abstract
The purpose of this paper is to study the existence and multiplicity of solutions to the following Kirchhoff equation with singular nonlinearity and Riemann-Liouville Fractional Derivative:
(P-lambda){ (a + b integral(T)(0)vertical bar D-0(t)alpha(u(t))vertical bar(p)dt)p-1 D-t(T)alpha(Phi p((0)D(t)(alpha)u(t)))
= lambda g(t)/u(gamma)(t) + f(t, u(t)), t is an element of (0, T);
u(0) = u(T) = 0,
where a >= 1, b, lambda > 0, p > 1 are constants, 1/p < alpha <= 1, 0 < gamma < 1, g is an element of C([0, 1]) and f is an element of C-1 ([0, T] x R, R). Under appropriate assumptions on the function f, we employ variational methods to show the existence and multiplicity of positive solutions of the above problem with respect to the parameter lambda.