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Solvability of higherorder BVPs in the halfline with unbounded nonlinearities
On higher order nonlinear impulsive boundary value problems
1.  Departamento de Matemática. Universidade de Évora, Centro de Investigação em Matemática e Aplicaçoes da U.E. (CIMAUE), Rua Romão Ramalho, 59. 7000671 Évora 
2.  Centro de Investigação em Matematica e Aplicações (CIMAUE), Instituto de Investigação e Formacão Avançada, Universidade de Évora, Rua Romão Ramalho, 59, 7000671 Évora, Portugal 
References:
[1] 
R. Agarwal, D. O'Regan, Multiple nonnegative solutions for second order impulsive diferential equations, Appl. Math. Comput. 155 (2000) 5159. Google Scholar 
[2] 
P. Chen, X. Tang, Existence and multiplicity of solutions for secondorder impulsive differential equations with Dirichlet problems, Appl. Math. Comput. 218 (2012) 177511789. Google Scholar 
[3] 
J. Fialho and F. Minhós, High Order Boundary Value Problems: Existence, Localization and Multiplicity Results, Mathematics Research Developments, Nova Science Publishers, Inc. New York, 2014 ISBN: 9781631177071. Google Scholar 
[4] 
J. R. Graef, L. Kong and F. Minhós, Higher order boundary value problems with phiLaplacian and functional boundary conditions, Comp. Math. Appl., 61 (2011) 236249. Google Scholar 
[5] 
M. R.Grossinho, F. Minhós and A.I. Santos, A note on a class of problems for a higherorder fully nonlinear equation under onesided Nagumotype condition, Nonlinear Anal., 70 (2009) 40274038. Google Scholar 
[6] 
X. Hao, L. Liu and Y. WU, Positive solutions for nthorder singular nonlocal boundary value problems, Boubd. Value Probl. (2007) 10, Article ID 74517. Google Scholar 
[7] 
V. Lakshmikantham, D. Baĭnov and P. Simeonov, Theory of impulsive differential equations. Series in Modern Applied Mathematics, 6. World Scientific Publishing Co., Inc., 1989. Google Scholar 
[8] 
X. Liu and D. Guo, Method of upper and lower solutions for secondorder impulsive integrodifferential equations in a Banach space, Comput. Math. Appl., 38 (1999), 213223. Google Scholar 
[9] 
Y. Liu and D. O'Regan, Multiplicity results using bifurcation techniques for a class of boundary value problems of impulsive differential equations, Commun. Nonlinear Sci. Numer. Simul. 16 (2011) 17691775. Google Scholar 
[10] 
B. Liu and J. Yu, Existence of solution for mpoint boundary value problems of secondorder differential systems with impulses, Appl. Math. Comput., 125, (2002), 155175 Google Scholar 
[11] 
R. Ma, B. Yang and Z. Wang, Positive periodic solutions of firstorder delay differential equations with impulses, Appl. Math. Comput. 219 (2013) 60746083. Google Scholar 
[12] 
J. Nieto and R. López, Boundary value problems for a class of impulsive functional equations, Comput. Math. Appl. 55 (2008) 27152731 Google Scholar 
[13] 
J. Nieto and D. O'Regan, Variational approach to impulsive differential equations, Nonlinear Anal. RWA, (2009), 680690. Google Scholar 
[14] 
A.M. Samoilenko and N.A. Perestyuk, Impulsive Differential Equations, World Scientific, Singapore, 1995. Google Scholar 
[15] 
Y. Tian and W. Ge, Variational methods to SturmLiouville boundary value problem for impulsive differential equations, Nonlinear Analysis: Theory, Methods & Applications, 72, (2010), 277287. Google Scholar 
[16] 
J. Xiao, J. Nieto and Z. Luo, Multiplicity of solutions for nonlinear second order impulsive differential equations with linear derivative dependence via variational methods, Communications in Nonlinear Science and Numerical Simulation, 17, (2012), 426432. Google Scholar 
[17] 
X. Zhang, M. Feng and W. Ge, Existence of solutions of boundary value problems with integral boundary conditions for secondorder impulsive integrodifferential equations in Banach spaces, J. Comput. Appl. Math, 233, (2010), 19151926 . Google Scholar 
show all references
References:
[1] 
R. Agarwal, D. O'Regan, Multiple nonnegative solutions for second order impulsive diferential equations, Appl. Math. Comput. 155 (2000) 5159. Google Scholar 
[2] 
P. Chen, X. Tang, Existence and multiplicity of solutions for secondorder impulsive differential equations with Dirichlet problems, Appl. Math. Comput. 218 (2012) 177511789. Google Scholar 
[3] 
J. Fialho and F. Minhós, High Order Boundary Value Problems: Existence, Localization and Multiplicity Results, Mathematics Research Developments, Nova Science Publishers, Inc. New York, 2014 ISBN: 9781631177071. Google Scholar 
[4] 
J. R. Graef, L. Kong and F. Minhós, Higher order boundary value problems with phiLaplacian and functional boundary conditions, Comp. Math. Appl., 61 (2011) 236249. Google Scholar 
[5] 
M. R.Grossinho, F. Minhós and A.I. Santos, A note on a class of problems for a higherorder fully nonlinear equation under onesided Nagumotype condition, Nonlinear Anal., 70 (2009) 40274038. Google Scholar 
[6] 
X. Hao, L. Liu and Y. WU, Positive solutions for nthorder singular nonlocal boundary value problems, Boubd. Value Probl. (2007) 10, Article ID 74517. Google Scholar 
[7] 
V. Lakshmikantham, D. Baĭnov and P. Simeonov, Theory of impulsive differential equations. Series in Modern Applied Mathematics, 6. World Scientific Publishing Co., Inc., 1989. Google Scholar 
[8] 
X. Liu and D. Guo, Method of upper and lower solutions for secondorder impulsive integrodifferential equations in a Banach space, Comput. Math. Appl., 38 (1999), 213223. Google Scholar 
[9] 
Y. Liu and D. O'Regan, Multiplicity results using bifurcation techniques for a class of boundary value problems of impulsive differential equations, Commun. Nonlinear Sci. Numer. Simul. 16 (2011) 17691775. Google Scholar 
[10] 
B. Liu and J. Yu, Existence of solution for mpoint boundary value problems of secondorder differential systems with impulses, Appl. Math. Comput., 125, (2002), 155175 Google Scholar 
[11] 
R. Ma, B. Yang and Z. Wang, Positive periodic solutions of firstorder delay differential equations with impulses, Appl. Math. Comput. 219 (2013) 60746083. Google Scholar 
[12] 
J. Nieto and R. López, Boundary value problems for a class of impulsive functional equations, Comput. Math. Appl. 55 (2008) 27152731 Google Scholar 
[13] 
J. Nieto and D. O'Regan, Variational approach to impulsive differential equations, Nonlinear Anal. RWA, (2009), 680690. Google Scholar 
[14] 
A.M. Samoilenko and N.A. Perestyuk, Impulsive Differential Equations, World Scientific, Singapore, 1995. Google Scholar 
[15] 
Y. Tian and W. Ge, Variational methods to SturmLiouville boundary value problem for impulsive differential equations, Nonlinear Analysis: Theory, Methods & Applications, 72, (2010), 277287. Google Scholar 
[16] 
J. Xiao, J. Nieto and Z. Luo, Multiplicity of solutions for nonlinear second order impulsive differential equations with linear derivative dependence via variational methods, Communications in Nonlinear Science and Numerical Simulation, 17, (2012), 426432. Google Scholar 
[17] 
X. Zhang, M. Feng and W. Ge, Existence of solutions of boundary value problems with integral boundary conditions for secondorder impulsive integrodifferential equations in Banach spaces, J. Comput. Appl. Math, 233, (2010), 19151926 . Google Scholar 
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