Abstract
In this work, we investigate the following nonlinear singular problem with Riemann-Liouville Fractional Derivative (P?) {-tD?1(?0D?t (u(t))?p-2 0D? tu(t)) = g(t)/u?(t) + ?f (t,u(t)) t ? (0,T); u(0) = u(T) = 0, where ? is a positive parameter, p > 1, 1/2 < ? ? 1,0 < ? < 1, g ? C([0,T]) and f?C([0,T] x R,R). Under appropriate assumptions on the function f, we employ the method of the Nehari manifold combined with the fibering maps in order to show the existence of ?0 such that for all ? ?(0,?0) the problem (P?) has at least two positive solutions. Finally, some examples are given to illustrate our results.
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