Solvability of periodic boundary value problem for fractional p-Laplacian equation

Abstract In this paper, we establish a continuation theorem for the fractional p -Laplacian operator with periodic boundary conditions. And then, we apply this continuation theorem to the study of periodic boundary value problem for fractional p -Laplacian equation. Under certain nonlinear growth condition of the nonlinearity, we obtain a new result on the existence of solutions.

[1]  D. O’Regan,et al.  Positive solutions for Dirichlet problems of singular nonlinear fractional differential equations , 2010 .

[2]  H. Srivastava,et al.  Theory and Applications of Fractional Differential Equations , 2006 .

[3]  Luigi Rodino,et al.  Existence and Uniqueness for a Nonlinear Fractional Differential Equation , 1996 .

[4]  Nickolai Kosmatov,et al.  A boundary value problem of fractional order at resonance. , 2010 .

[5]  J. Trujillo,et al.  Differential equations of fractional order:methods results and problem —I , 2001 .

[6]  O. Agrawal,et al.  Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering , 2007 .

[7]  Varsha Daftardar-Gejji,et al.  Existence of positive solutions of nonlinear fractional differential equations , 2003 .

[8]  Wenbin Liu,et al.  MULTIPLE PERIODIC SOLUTIONS OF p-LAPLACIAN EQUATION WITH ONE-SIDE NAGUMO CONDITION , 2008 .

[9]  Wenbin Liu,et al.  A boundary value problem for fractional differential equation with p-Laplacian operator at resonance☆ , 2012 .

[10]  M. Benchohra,et al.  Boundary value problems for differential equations with fractional order and nonlocal conditions , 2009 .

[11]  Zhanbing Bai.  On solutions of some fractional $m$-point boundary value problems at resonance , 2010 .

[12]  Xinwei Su,et al.  Boundary value problem for a coupled system of nonlinear fractional differential equations , 2009, Appl. Math. Lett..

[13]  H. Su,et al.  Positive solutions of four-point boundary value problems for higher-order p-Laplacian operator , 2007 .

[15]  Wenbin Liu,et al.  Antiperiodic Solutions for Li´ enard-Type Differential Equation with p-Laplacian Operator , 2010 .

[16]  Jean Mawhin,et al.  Periodic solutions for nonlinear systems with p-Laplacian-like operators , 1998 .

[17]  I. Podlubny.  Fractional differential equations , 1998 .

[18]  Weigao Ge,et al.  Solvability of nonlocal boundary value problems for ordinary differential equation of higher order with a p-Laplacian , 2008, Computers and Mathematics with Applications.

[19]  Weihua Jiang,et al.  The existence of solutions to boundary value problems of fractional differential equations at resona , 2011 .

[20]  Wenbin Liu,et al.  An anti-periodic boundary value problem for the fractional differential equation with a p-Laplacian operator , 2012, Appl. Math. Lett..

[21]  Zhanbing Bai,et al.  Positive solutions for boundary value problem of nonlinear fractional differential equation , 2005 .

[22]  O. Marichev,et al.  Fractional Integrals and Derivatives: Theory and Applications , 1993 .

[23]  Juan J. Nieto,et al.  Nontrivial solutions for a nonlinear multi-point boundary value problem of fractional order , 2010, Comput. Math. Appl..

[24]  Wenbin Liu,et al.  Antiperiodic Solutions for Liénard-Type Differential Equation with -Laplacian Operator , 2010 .

[25]  D. Jiang,et al.  Upper and Lower Solution Method and a Singular Boundary Value Problem for the One-Dimensional p-Laplacian , 2000 .

[26]  K. Miller,et al.  An Introduction to the Fractional Calculus and Fractional Differential Equations , 1993 .

[27]  Mohamed Abdalla Darwish,et al.  On initial and boundary value problems for fractional order mixed type functional differential inclusions , 2010, Comput. Math. Appl..