[1] Wei Z L. Some necessary and sufficient conditions for existence of positive solutions for third order singular sublinear multi-point boundary value problems. Acta Mathematica Scientia, 2014, 34B(6):1795-1810
[2] O'Regan D. Theory of Singular Boundary Value Problems. Singapore:World Scientific Press, 1994
[3] Agarwal R P, O'Regan D. Singular Differential and Integral Equations with Applications. Dordrecht:Kluwer Academic Publishers, 2003
[4] Agarwal R P, O'Regan D. Singular boundary value problems for superlinear second order ordinary and delay differential equations. Journal of Differential Equations. 1996, 130:333-355
[5] Agarwal R P, Perera K, O'Regan D. Multiple positive solutions of singular problems by variational methods. Proceedings of The American Mathematical Society, 2006, 134:817-824
[6] Agarwal R P, Perera K, O'Regan D. Multiple positive solutions of singular and nonsingular discrete problems via variational methods. Nonlinear Analysis:Theory, Methods and Applications, 2004, 58:69-73
[7] Liu J, Zhao Z Q. An application of variational methods to singular problems. Electronic Journal of Differential Equations, 2014, 135:1-9
[8] Tian Y, Ge W G. Applications of variational methods to boundary value problem for impulsive differential equations. Proceedings of Edinburgh Mathematical Society, 2008, 51:509-527
[9] Nieto J J, Rodriguez-Lopez R. Boundary value problems for a class of impulsive functional equations. Computers and Mathematics with Application, 2008, 55:2715-2731.
[10] Nieto J J, O'Regan D. Variational approach to impulsive differential equations. Nonlinear Analysis, Real World Application, 2009, 10:680-690
[11] Zhang D. Multiple solutions of nonlinear impulsive differential equations with Dirichlet boundary conditions via variational method. Results in Mathematics, 2013, 63:611-628
[12] Zhang D, Dai B X, Chen Y M. Existence of solutions for a damped nonlinear impulsive problem with Dirichlet boundary conditions. Mathematical Methods in the Applied Sciences, 2014, 37:1538-1552
[13] Dai B X, Zhang D. The existence and multiplicity of solutions for second-order impulsive differential equations on the half-line. Results in Mathematics, 2013, 63:135-149
[14] Liu J, Zhao Z Q. An application of variational methods to second-order impulsive differential equation with derivative dependence. Electronic Journal of Differential Equations, 2014, 62:1-13
[15] Mawhin J, Willem M. Critical Point Theory and Hamiltonian Systems. Berlin:Springer-Verlag, 1989
[16] Zeidler. Nonlinear Functional Analysis and its Applications. Berlin:Springer-Verlag, 1985 |