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Ground state solutions for two classes of fractional Hamiltonian systems | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقالات آماده انتشار، اصلاح شده برای چاپ، انتشار آنلاین از تاریخ 26 فروردین 1405 اصل مقاله (430.59 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2025.28026.3784 | ||
| نویسنده | ||
| Mohsen Timoumi* | ||
| Dpt of Mathematics, Faculty of Sciences of Monastir, 5000 Monastir, Tunisia | ||
| تاریخ دریافت: 15 مرداد 1401، تاریخ بازنگری: 22 خرداد 1402، تاریخ پذیرش: 27 بهمن 1403 | ||
| چکیده | ||
| In this paper, we are concerned with the following periodic fractional Hamiltonian system $$\left\{ \begin{array}{l} _{t}D_{\infty}^{\alpha}(_{-\infty}D_{t}^{\alpha}u)(t)+L(t)u(t)=\nabla W(t,u(t)),\ t\in\mathbb{R}\\ u\in H^{\alpha}(\mathbb{R}). \end{array}\right.$$ Using variational methods and a version of the concentration compactness principle, we study the existence of ground state solutions for this system under two different classes of superquadratic conditions weaker than the ones known in the literature. To the best of our knowledge, there has been no work focused in this case. | ||
| کلیدواژهها | ||
| Fractional Hamiltonian systems؛ ground state orbits؛ periodic potentials؛ variational methods؛ concentration compactness principle | ||
| مراجع | ||
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[1] O. Agrawal, J. Tenreiro Machado, and J. Sabatier, Fractional Derivatives and Their Applications, Nonlinear dynamics, Springer-Verlag, Berlin, 2004.
[2] N. Nyamoradi, A. Alsaedi, B. Ahmad, and Y. Zou, Multiplicity of homoclinic solutions for fractional Hamiltonian systems with subquadratic potential, Entropy 19 (2017), no. 50, 1-24.
[3] N. Nyamoradi, A. Alsaedi, B. Ahmad, and Y. Zou, Variational approach to homoclinic solutions for fractional Hamiltonian systems, J. Optim. Theory Appl. 174 (2017), no. 1, 223-237.
[4] Z. Bai and H. Lü, Positive solutions for boundary value problem of nonlinear fractional differential equation, J. Math. Anal. Appl. 311 (2005), 495-505.
[5] Z. Bai and Y. Zhang, The existence of solutions for a fractional multi-point boundary value problem, Comput. Math. Appl. 69 (2010), 2364-2372.
[6] Y. He, D. Qin, and D. Chen, Ground state solutions for Hamiltonian elliptic systems with super or asymptotically quadratic nonlinearity, Boundary Value Problems 2019 (2019), no. 158, 1-20.
[7] Y. Li and B. Dai, Existence and multiplicity of nontrivial solutions for Liouville-Weyl fractional nonlinear Schrödinger equation, RA SAM 112 (2018), 957-967.
[8] Y. Ding and S. Luan, Multiple solutions for a class of nonlinear Schrödinger equations, J. Differ. Equ. 207 (2004), 423-457.
[9] D.E. Edmunds and W.D. Evans, Spectral Theory and Differential Operators, Clarendon Press, Oxford, 1987.
[10] R. Hiffer, Applications of Fractional Calculus in Physics, World Science, Singapore, 2000.
[11] W. Jiang, The existence of solutions for boundary value problems of fractional differential equations at resonance, Nonlinear Anal. 74 (2011), 1987-1994.
[12] F. Jiao and Y. Zhou, Existence results for fractional boundary value problem via critical point theory, Int. J. Bif. and Chaos 22 (2012), no. 4, 1-17.
[13] S. G. Samko, A.A. Kilbas, and O.I. Marichev, Fractional Integrals and Derivatives, Theory and Applications, Gordon and Breach, Switzerland, 1993.
[14] A.A. Kilbas, H.M. Srivastava, and J.J. Trujillo, Theory and applications of fractional differential equations, North-Holland Mathematical Studies 204, Singapore 2006.
[15] W. Kryszewski and S. Szulkin, Generalized linking theorem with an application to a semilinear Schrödinger equation, Adv. Differ. Equ. 3 (1998), no. 3, 441-472.
[16] G. Li and A. Szulkin, An asymptotically periodic Schrödinger equation with indefinite linear part, Comm. Contem. Math. 4 (2002), no. 4, 763-776.
[17] S. Liang and J. Zhang, Positive solutions for boundary value problems of nonlinear fractional differential equations, Nonlinear Anal. 71 (2009), 5545-5550.
[18] P.L. Lions, The concentration-compactness principle in the calculus of variations. The locally compact cases, Part II, Ann. Inst. Henri Poincaré 1 (1984), no. 4, 223-283.
[19] J. Mawhin and M. Willem, Critical Point Theory and Hamiltonian Systems, Applied Mathematical Sciences, Springer, Berlin, 1989.
[20] A. Mendez, C. Torres, Multiplicity of solutions for fractional Hamiltonian systems with Liouville-Weyl fractional derivative, Fract. Calc. Appl. Anal. 18 (2015), 875-890.
[21] K. Miller and B. Ross, An Introduction to Differential Equations, Wiley and Sons, New York, 1993.
[22] A. Pankov, Periodic nonlinear Schrödinger equation with application to photonic crystals, Milan J. Math. 73 (2005), 259-287.
[23] I. Pollubny, Fractional Differential Equations, Academic Press, 1999.
[24] P.H. Rabinowitz, Minimax methods in critical point theory with applications to differential equations, in: CBMS Reg. Conf. Ser. in Math. 65, American Mathematical Society, Providence, R.I, 1986.
[25] M. Schechter and W. Zou, Weak linking theorems and Schrödinger equations with critical Sobolev exponent, ESAIM: Control Optim. Calc. Var. 9 (2003), 601-619.
[26] M. Struwe, Variational Methods, Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems, Springer-Verlag, Berlin, 2000.
[27] A. Szulkin and T. Weth, Ground state solutions for some indefinite variational problems, J. Funct. Anal. 257 (2009), 3802-3822.
[28] X. Tang, Ground state solutions of Nehari-Pankov type for a superlinear Hamiltonian elliptic system on R^N, Cand. Math. Bull. 58 (2015), no. 3, 651-663.
[29] X.H. Tang, Non-Nehari manifold method for asymptotically periodic Schrödinger equations, Sci. China Math. 58 (2015), no. 4, 715-728.
[30] K. Teng, Multiple homoclinic solutions for a class of fractional Hamiltonian systems, Progr. Fract. Diff. Appl. 2 (2016), no. 4, 265-276.
[31] M. Timoumi, Ground state solutions for a class of superquadratic fractional Hamiltonian systems, J. Ellipt. Parab. Equ. 7 (2021), 171-197.
[32] M. Timoumi, Infinitely many solutions for a class of superquadratic fractional Hamiltonian systems, Fract. Differ. Calc. 8 (2018), no. 2, 309-326.
[33] M. Timoumi, Multiple many solutions for a class of superquadratic fractional Hamiltonian systems, Univ. J. Math. Appl. 1 (2018), no. 3, 186-195.
[34] C. Torres, Existence of solutions for fractional Hamiltonian systems, Electr. J. Diff. Eq. 2013 (2013), no. 259, 1-12.
[35] C. Torres Ledesma, Existence of solutions for fractional Hamiltonian systems with nonlinear derivative dependence in R, J. Fract. Calc. Appl. 7 (2016), no. 2, 74-87.
[36] C. Torres, Ground state solution for differential equations with left and right fractional derivatives, Math. Meth. Appl. Sci. 38 (2015), 5063-5073.
[37] M. Willem, Progress in Nonlinear Differential Equations and Their Applications, Minimax Theorems, Birkhauser 1996.
[38] X. Wu and Z. Zhang, Solutions for perturbed fractional Hamiltonian systems without coercive conditions, Boundary Value Problems 2015 (2015), no. 149, 1-12.
[39] Z. Zhang and R. Yuan, Existence of solutions to fractional Hamiltonian systems with combined nonlinearities, Electr. J. Diff. Eq. 2016 (2016), no. 40, 1-13.
[40] Z. Zhang and R. Yuan, Solutions for subquadratic fractional Hamiltonian systems without coercive conditions, Math. Meth. Appl. Sci. 37 (2014), 2934-2945.
[41] Z. Zhang and R. Yuan, Variational approach to solutions for a class of fractional Hamiltonian systems, Math. Meth. Appl. Sci. 37 (2014), 1873-1883.
[42] S. Zhang, Existence of solutions for a boundary value problems of fractional differential equations at resonance, Nonlinear Anal. 74 (2011), 1987-1994.
[43] S. Zhang, Existence of solutions for the fractional equations with nonlinear boundary conditions, Comput. Math. Appl. 61 (2011), 1202-1208. | ||
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