Abstract
In this paper, we probe into the solvability of Sturm-Liouville problem for fractional advection-dispersion equations without traditional Ambrosetti-Rabinowitz conditions. Some existence results of infinitely many small negative energy and large energy solutions are obtained by employing variant fountain theorems. The nonlinearity $f$ and $l_i$ ($i$=1,2,..., $m$) are considered under certain appropriate assumptions which are distinct from those assumed in previous articles. In addition, the main result is confirmed by an example which is provided.
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