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| 摘要: |
本文研究一类带组合项的分数阶边值问题
{u（0）=0，u（T）=0，-d/dt（1/20Dt-β（u'（t））+1/2 tDT-β（u'（t）））=▽W（t，u（t））a.e.t ∈[0，T]，
其中W在无穷远处是一个超二次和次二次的组合.利用山路引理和Ekeland变分原理，得到上述问题至少存在两个非平凡解，推广和发展了已有文献中的结果. |
| 关键词: 分数阶边值问题 山路引理 Ekeland变分原理 |
| DOI： |
| 分类号:O175.8 |
| 基金项目:国家自然科学基金资助（11571176；11701289）. |
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| TWO SOLUTIONS FOR A CLASS OF FRACTIONAL BOUNDARY VALUE PROBLEMS WITH MIXED NONLINEARITIES |
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LI Shan-shan,WANG Zhi-yong
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| Abstract: |
In this paper, we deal with the following kind of fractional boundary value problems with mixed nonlinearities
{u(0)=0, u(T)=0,-d/dt(1/20Dt-β(u'(t)) + 1/2 tDT-β(u'(t)))=▽W (t, u(t)) a.e. t ∈[0, T],
where W is a combination of superquadratic and subquadratic terms. By using mountain pass lemma and Ekeland's variational principle, we prove that the above boundary value problem has at least two nontrivial solutions, which extends and improves some existed literature. |
| Key words: fractional boundary value problem mountain pass lemma Ekeland's variational principle |
