We consider a class of discrete nonlinear Schrodinger (DNLS) equations in m dimensional lattices with partially sublinear nonlinearity f. Combining variational methods and a priori estimate, we give a general sufficient condition on f for type (A), that is, a sequence of nontrivial homoclinic solutions accumulating to zero. By using a compact embedding technique, we overcome the loss of compactness due to the problem being set on the unbounded domain Z(m). Another obstacle caused by the local definition of f is solved by using the cutoff methods to recover the global property of f. To the best of our knowledge, this is the first time to obtain infinitely many homoclinic solutions for the DNLS equations with partially sublinear nonlinearity. Moreover, we prove that if f is not sublinear, the zero solution is isolated from other homoclinic solutions. Our results show that the sublinearity and oddness of f yield type (A). Without the oddness assumption, we still can prove that this problem has at least a nontrivial homoclinic solution if f is local sublinear, which improves some existing results.
机构:
Hunan Agr Univ, Oriental Sci & Technol Coll, Changsha 410128, Hunan, Peoples R China
Hunan Agr Univ, Coll Sci, Changsha 410128, Hunan, Peoples R ChinaHunan Agr Univ, Oriental Sci & Technol Coll, Changsha 410128, Hunan, Peoples R China
Liu, Xia
Zhou, Tao
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South China Univ Technol, Sch Business Adm, Guangzhou 510640, Guangdong, Peoples R ChinaHunan Agr Univ, Oriental Sci & Technol Coll, Changsha 410128, Hunan, Peoples R China
Zhou, Tao
Shi, Haiping
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Guangdong Construct Polytech, Modern Business & Management Dept, Guangzhou 510440, Guangdong, Peoples R ChinaHunan Agr Univ, Oriental Sci & Technol Coll, Changsha 410128, Hunan, Peoples R China
机构:
Univ Jinan, Sch Math Sci, Jinan 250022, Shandong, Peoples R ChinaUniv Jinan, Sch Math Sci, Jinan 250022, Shandong, Peoples R China
Chen, Guanwei
Ma, Shiwang
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Nankai Univ, Sch Math Sci, Tianjin 300071, Peoples R China
Nankai Univ, LPMC, Tianjin 300071, Peoples R ChinaUniv Jinan, Sch Math Sci, Jinan 250022, Shandong, Peoples R China
Ma, Shiwang
Wang, Zhi-Qiang
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Utah State Univ, Dept Math & Stat, Logan, UT 84322 USAUniv Jinan, Sch Math Sci, Jinan 250022, Shandong, Peoples R China
机构:
Hunan Agr Univ, Oriental Sci & Technol Coll, Changsha 410128, Hunan, Peoples R China
Hunan Agr Univ, Coll Sci, Changsha 410128, Hunan, Peoples R ChinaHunan Agr Univ, Oriental Sci & Technol Coll, Changsha 410128, Hunan, Peoples R China
Liu, Xia
Zhou, Tao
论文数: 0引用数: 0
h-index: 0
机构:
South China Univ Technol, Sch Business Adm, Guangzhou 510640, Guangdong, Peoples R ChinaHunan Agr Univ, Oriental Sci & Technol Coll, Changsha 410128, Hunan, Peoples R China
Zhou, Tao
Shi, Haiping
论文数: 0引用数: 0
h-index: 0
机构:
Guangdong Construct Polytech, Modern Business & Management Dept, Guangzhou 510440, Guangdong, Peoples R ChinaHunan Agr Univ, Oriental Sci & Technol Coll, Changsha 410128, Hunan, Peoples R China
机构:
Univ Jinan, Sch Math Sci, Jinan 250022, Shandong, Peoples R ChinaUniv Jinan, Sch Math Sci, Jinan 250022, Shandong, Peoples R China
Chen, Guanwei
Ma, Shiwang
论文数: 0引用数: 0
h-index: 0
机构:
Nankai Univ, Sch Math Sci, Tianjin 300071, Peoples R China
Nankai Univ, LPMC, Tianjin 300071, Peoples R ChinaUniv Jinan, Sch Math Sci, Jinan 250022, Shandong, Peoples R China
Ma, Shiwang
Wang, Zhi-Qiang
论文数: 0引用数: 0
h-index: 0
机构:
Utah State Univ, Dept Math & Stat, Logan, UT 84322 USAUniv Jinan, Sch Math Sci, Jinan 250022, Shandong, Peoples R China