Multiple solutions for a class of superquadratic fractional Hamiltonian systems

Mohsen Timoumi

doi:https://doi.org/10.32323/ujma.388067

Makale detayları

Multiple solutions for a class of superquadratic fractional Hamiltonian systems

Yazarlar:

Mohsen Timoumi

Yayıncı:

Emrah Evren KARA

Ana Başlıklar:

Matematik

Dergi:

Universal Journal of Mathematics and Applications 2018 Vol.1 Issue 3, pp.186-195

Belge Tipi:

Makale

Yayın Tarihi:

9/2018

Belge Dili:

İngilizce

Document ID (Org No.):

2000670185

Sıklık:

Üç Aylık

pISSN:

2619-9653

DOI:

https://doi.org/10.32323/ujma.388067

Özet:

 


In this paper, we are concerned with the existence of solutions for a class of fractional Hamiltonian systems {tDα∞(−∞Dαtu)(t)+L(t)u(t)=∇W(t,u(t)), t∈Ru∈Hα(R, RN),{tD∞α(−∞Dtαu)(t)+L(t)u(t)=∇W(t,u(t)), t∈Ru∈Hα(R, RN),\left\{ \begin{array}{l} _{t}D_{\infty}^{\alpha}(_{-\infty}D_{t}^{\alpha}u)(t)+L(t)u(t)=\nabla W(t,u(t)),\ t\in\mathbb{R}\\ u\in H^{\alpha}(\mathbb{R},\ \mathbb{R}^{N}), \end{array}\right.  where tDα∞tD∞α_{t}D_{\infty}^{\alpha} and −∞Dαt−∞Dtα_{-\infty}D^{\alpha}_{t} are the Liouville-Weyl fractional derivatives of order 12<α<112<α<1\frac{1}{2}<\alpha<1, L∈C(R,RN2)L∈C(R,RN2)L\in C(\mathbb{R},\mathbb{R}^{N^{2}}) is a symmetric matrix-valued function and W(t,x)∈C1(R×RN,R)W(t,x)∈C1(R×RN,R)W(t,x)\in C^{1}(\mathbb{R}\times\mathbb{R}^{N},\mathbb{R}). Applying a Symmetric Mountain Pass Theorem, we prove the existence of infinitely many solutions for (1) when LLL is not required to be either uniformly positive definite or coercive and W(t,x)W(t,x)W(t,x) satisfies some weaker superquadratic conditions at infinity in the second variable but does not satisfy the well-known Ambrosetti-Rabinowitz superquadratic growth condition.

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Makale detayları

Multiple solutions for a class of superquadratic fractional Hamiltonian systems

Yazarlar: Mohsen Timoumi

Yayıncı: Emrah Evren KARA

Ana Başlıklar: Matematik

Dergi: Universal Journal of Mathematics and Applications 2018 Vol.1 Issue 3, pp.186-195

Belge Tipi: Makale

Yayın Tarihi: 9/2018

Belge Dili: İngilizce

Document ID (Org No.): 2000670185

Sıklık: Üç Aylık

pISSN: 2619-9653

DOI: https://doi.org/10.32323/ujma.388067

Sayı

Yazarlar:

Mohsen Timoumi

Yayıncı:

Emrah Evren KARA

Ana Başlıklar:

Matematik

Dergi:

Universal Journal of Mathematics and Applications 2018 Vol.1 Issue 3, pp.186-195

Belge Tipi:

Makale

Yayın Tarihi:

9/2018

Belge Dili:

İngilizce

Document ID (Org No.):

2000670185

Sıklık:

Üç Aylık

pISSN:

2619-9653

DOI:

https://doi.org/10.32323/ujma.388067