On nonlinear perturbations of a periodic integrodifferential equation with critical exponential growth

References

• Caffarelli LA, Silvestre L. An extension problems related to the fractional Laplacian. Commun PDE. 2007;36:1245–1260.
   Web of Science ®Google Scholar
• Secchi S. Ground state solutions for nonlinear fractional Schrödinger equations in RN. J Math Phys. 2013;54:17.
   Web of Science ®Google Scholar
• Alberti G, Bellettini G. A nonlocal anisotropic model for phase transitions. Math Ann. 1998;310:527–560.
   Web of Science ®Google Scholar
• Gilboa G, Osher S. Nonlocal operators with applications to image processing. Multiscale Model Simul. 2008;7:1005–1028.
   Web of Science ®Google Scholar
• Di Nezza E, Palatucci G, Valdinoci E. Hitchhiker's guide to the fractional Sobolev spaces. Bull Sci Math. 2012;136:521–573.
   Web of Science ®Google Scholar
• Cheng M. Bound state for the fractional Schrödinger equation with unbounded potential. J Math Phys. 2012;53:7.
   Web of Science ®Google Scholar
• Felmer P, Quaas A, Tan J. Positive solutions of nonlinear Schrödinger equation with the fractional Laplacian. Proc R Soc Edinb A. 2012;142:1237–1262.
   Google Scholar
• Ozawa T. On critical cases of Sobolev's inequalities. J Funct Anal. 1995;127:259–269.
   Web of Science ®Google Scholar
• Iula S. A note on the Moser-Trudinger inequality in Sobolev-Slobodeckij spaces in dimension one. Atti Accad Naz Lincei Rend Lincei Mat Appl. 2017;28:871–884.
   Google Scholar
• Kozono H, Sato T, Wadade H. Upper bound of the best constant of a Trudinger-Moser inequality and its application to a Gagliardo-Nirenberg inequality. Indiana Univ Math J. 2006;55:1951–1974.
   Web of Science ®Google Scholar
• Takahashi F. Critical and subcritical fractional Trudinger-Moser-type inequalities on R. Adv Nonlinear Anal. 2019;8:868–884.
   Web of Science ®Google Scholar
• Moser J. A sharp form of an inequality by N. Trudinger Indiana Univ Math J. 1971;20:1077–1092.
   Web of Science ®Google Scholar
• Trudinger NS. On imbeddings into Orlicz spaces and some applications. J Math Mech. 1967;17:473–484.
   Web of Science ®Google Scholar
• M. de Souza M, Araújo YL. On nonlinear perturbations of a periodic fractional Schrödinger equation with critical exponential growth. Math Nachr. 2016;289:610–625.
   Web of Science ®Google Scholar
• Alves CO, Miyagaki O. On nonlinear perturbations of a periodic elliptic problem in R2 involving critical growth. Nonlinear Anal. 2004;56:781–791.
   Web of Science ®Google Scholar
• Frassu S. Nonlinear Dirichlet problem for the non-local anisotropic operator LK. Commun Pure Appl Anal. 2019;18:1847–1867.
   Web of Science ®Google Scholar
• Kassmann M. A priori estimates for integro-differential operators with measurable kernels. Calc Var PDE. 2009;34:1–21.
   Web of Science ®Google Scholar
• R. Mikulevičius R, Pragarauskas H. On the Cauchy problem for certain integro-differential operators in Sobolev and Hölder spaces inequality and its application to a Gagliardo-Nirenberg inequality. Lithuanian Math J. 1992;32:238–264.
   Google Scholar
• Bahrouni A. Trudinger-Moser inequality and existence of solution for perturbed non-local elliptic operators with exponential nonlinearity. Commun Pure Appl Anal. 2017;16:243–252.
   Web of Science ®Google Scholar
• Duarte RC, Souto MAS. Nonlocal Schrödinger equations for integro-differential operators with measurable kernels. Topol Meth Nonlinear Anal. 2019;54:383–406.
   Web of Science ®Google Scholar
• Fiscella A. Saddle point solutions for non-local elliptic operators. Topol Meth Nonlinear Anal. 2014;44:527–538.
   Web of Science ®Google Scholar
• Fiscella A, Servadei R, Valdinoci E. A resonance problem for non-local elliptic operators. Z Anal Anwend. 2013;32:411–431.
   Web of Science ®Google Scholar
• Fiscella A, Servadei R, Valdinoci E. Density properties for fractional Sobolev spaces. Ann Acad Sci Fenn Math. 2015;40:235–253.
   Google Scholar
• Servadei R. The Yamabe equation in a non-local setting. Adv Nonlinear Anal. 2013;2:235–270.
   Web of Science ®Google Scholar
• Servadei R, Valdinoci E. Mountain Pass solutions for non-local elliptic operators. J Math Anal Appl. 2012;389:887–898.
   Web of Science ®Google Scholar
• Servadei R, Valdinoci E. Variational methods for non-local operators of elliptic type. Discrete Contin Dyn Syst. 2013;33:2105–2137.
   Web of Science ®Google Scholar
• Servadei R, Valdinoci E. The Brezis-Nirenberg result for the fractional Laplacian. Trans Amer Math Soc. 2015;367:67–102.
   Web of Science ®Google Scholar
• Thin NV. Singular Trudinger-Moser inequality and fractional p−Laplace equations in RN. Nonlinear Anal. 2020;196:28.
   Web of Science ®Google Scholar
• Alves CO, Souto MAS. Existence of solutions for a class of elliptic equations in RN with vanishing potentials. J Differ Equ. 2012;252:5555–5568.
   Web of Science ®Google Scholar
• M. de Souza M, Araújo YL. On a class of fractional Schrödinger equations in with sign-changing potential. Appl Anal. 2017;97:538–551.
   Web of Science ®Google Scholar
• Pucci P, Xiang M, Zhang B. Multiple solutions for nonhomogeneous Schrödinger-Kirchhoff type equations involving the fractional p-Laplacian in RN. Calc Var Partial Differ Equ. 2015;54:2785–2806.
   Web of Science ®Google Scholar
• Servadei R, Valdinoci E. Lewy-Stampacchia type estimates for variational inequalities driven by (non)local operators. Rev Mat Iberoam. 2013;29:1091–1126.
   Web of Science ®Google Scholar
• Brézis H. Functional analysis sobolev, spaces and partial differential equations. Berlin: Springer Science; 2010.
   Google Scholar
• Mawhin J, Willem M. Critical point theory and Hamiltonian systems. New York: Applied Mathematical Sciences; 1989.
   Google Scholar
• Lions PL. Symétrie et compacité dans les espaces de Sobolev. J Funct Anal. 1982;49:315–334.
   Web of Science ®Google Scholar
• Brézis H, Lieb E. A relation between pointwise convergence of functions and convergence of functionals. Proc Amer Math Soc. 1983;88:486–490.
   Web of Science ®Google Scholar
• de Figueiredo DG, Ruf B. Elliptic equations in R2 with nonlinearities in the critical growth range. Calc Var Partial Differ Equ. 1995;3:139–153.
   Web of Science ®Google Scholar