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Solvability of higherorder BVPs in the halfline with unbounded nonlinearities
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 Matemática e Aplicações (CIMAUE), Portugal 
References:
[1] 
R.P. Agarwal and D. O'Regan, Infinite Interval Problems for Differential, Difference and Integral Equations, Kluwer Academic Publisher, Glasgow 2001. Google Scholar 
[2] 
R.P. Agarwal and D. O'Regan, Nonlinear boundary value problems on the semiinfinite interval: an upper and lower solution approach, Mathematika 49, no. 12, (2002) 129140. Google Scholar 
[3] 
C. Bai and C. Li, Unbounded upper and lower solution method for thirdorder boundaryvalue problems on the halfline Electronic Journal of Differential Equations, 119 (2009), 112. Google Scholar 
[4] 
F. Bernis and L.A. Peletier, Two problems from draining flows involving thirdorder ordinary differential equations SIAM J. Math. Anal., 27 (1996), 515527. Google Scholar 
[5] 
A. Cabada, F. Minhós and A. I. Santos, Solvability for a third order discontinuous fully equation with functional boundary conditions J. Math. Anal. Appl., 322 (2006), 735748. Google Scholar 
[6] 
P.W. Eloe, E. R. Kaufmann and C. C. Tisdell, Multiple solutions of a boundary value problem on an unbounded domain, Dynamic Systems and Applications, 15 (2006), 5363. Google Scholar 
[7] 
J. Fialho and F. Minhós, Existence and location results for hinged beams with unbounded nonlinearities, Nonlinear Anal., 71 (2009), 15191525. Google Scholar 
[8] 
J. Graef, L. Kong and F. Minhós, Higher order boundary value problems with ÎLaplacian and functional boundary conditions , Computers and Mathematics with Applications, 61 (2011), 236249. Google Scholar 
[9] 
M. Greguš, Third Order Linear Differential Equations, Mathematics and its Applications, Reidel Publishing Co., Dordrecht, 1987. Google Scholar 
[10] 
M. R. Grossinho, F. Minhós and A. I. Santos, A note on a class of problems for a higher order fully nonlinear equation under one sided Nagumo type condition, Nonlinear Anal., 70 (2009), 40274038. Google Scholar 
[11] 
H. Lian, P. Wang and W. Ge, Unbounded upper and lower solutions method for SturmLiouville boundary value problem on infinite intervals, Nonlinear Anal., 70 (2009), 26272633. Google Scholar 
[12] 
H. Lian and J. Zhao, Existence of Unbounded Solutions for a ThirdOrder Boundary Value Problem on Infinite Intervals, Discrete Dynamics in Nature and Society, 2012, Article ID 357697, 14 pages. Google Scholar 
[13] 
F. Minhós, Location results: an under used tool in higher order boundary value problems, International Conference on Boundary Value Problems: Mathematical Models in Engineering, Biology and Medicine, American Institute of Physics Conference Proceedings, 1124 (2009), 244253. Google Scholar 
[14] 
F. Minhós, T. Gyulov and A. I. Santos, Lower and upper solutions for a fully nonlinear beam equations, Nonlinear Anal., 71 (2009), 281292. Google Scholar 
[15] 
W. C. Troy, Solutions of thirdorder differential equations relevant to draining and coating flows, SIAM J. Math. Anal., 24 (1993), 155171. Google Scholar 
[16] 
E.O. Tuck and L.W. Schwartz, A boundary value problem from draining and coating flows involving a thirdorder differential equation relevant to draining and coating flows, SIAM Rev., 32 (1990), 453469. Google Scholar 
[17] 
B. Yan, D. O'Regan and R.P. Agarwal, Unbounded solutions for singular boundary value problems on the semiinfinite interval: Upper and lower solutions and multiplicity, J.Comput.Appl.Math., 197 (2006), 365386. Google Scholar 
show all references
References:
[1] 
R.P. Agarwal and D. O'Regan, Infinite Interval Problems for Differential, Difference and Integral Equations, Kluwer Academic Publisher, Glasgow 2001. Google Scholar 
[2] 
R.P. Agarwal and D. O'Regan, Nonlinear boundary value problems on the semiinfinite interval: an upper and lower solution approach, Mathematika 49, no. 12, (2002) 129140. Google Scholar 
[3] 
C. Bai and C. Li, Unbounded upper and lower solution method for thirdorder boundaryvalue problems on the halfline Electronic Journal of Differential Equations, 119 (2009), 112. Google Scholar 
[4] 
F. Bernis and L.A. Peletier, Two problems from draining flows involving thirdorder ordinary differential equations SIAM J. Math. Anal., 27 (1996), 515527. Google Scholar 
[5] 
A. Cabada, F. Minhós and A. I. Santos, Solvability for a third order discontinuous fully equation with functional boundary conditions J. Math. Anal. Appl., 322 (2006), 735748. Google Scholar 
[6] 
P.W. Eloe, E. R. Kaufmann and C. C. Tisdell, Multiple solutions of a boundary value problem on an unbounded domain, Dynamic Systems and Applications, 15 (2006), 5363. Google Scholar 
[7] 
J. Fialho and F. Minhós, Existence and location results for hinged beams with unbounded nonlinearities, Nonlinear Anal., 71 (2009), 15191525. Google Scholar 
[8] 
J. Graef, L. Kong and F. Minhós, Higher order boundary value problems with ÎLaplacian and functional boundary conditions , Computers and Mathematics with Applications, 61 (2011), 236249. Google Scholar 
[9] 
M. Greguš, Third Order Linear Differential Equations, Mathematics and its Applications, Reidel Publishing Co., Dordrecht, 1987. Google Scholar 
[10] 
M. R. Grossinho, F. Minhós and A. I. Santos, A note on a class of problems for a higher order fully nonlinear equation under one sided Nagumo type condition, Nonlinear Anal., 70 (2009), 40274038. Google Scholar 
[11] 
H. Lian, P. Wang and W. Ge, Unbounded upper and lower solutions method for SturmLiouville boundary value problem on infinite intervals, Nonlinear Anal., 70 (2009), 26272633. Google Scholar 
[12] 
H. Lian and J. Zhao, Existence of Unbounded Solutions for a ThirdOrder Boundary Value Problem on Infinite Intervals, Discrete Dynamics in Nature and Society, 2012, Article ID 357697, 14 pages. Google Scholar 
[13] 
F. Minhós, Location results: an under used tool in higher order boundary value problems, International Conference on Boundary Value Problems: Mathematical Models in Engineering, Biology and Medicine, American Institute of Physics Conference Proceedings, 1124 (2009), 244253. Google Scholar 
[14] 
F. Minhós, T. Gyulov and A. I. Santos, Lower and upper solutions for a fully nonlinear beam equations, Nonlinear Anal., 71 (2009), 281292. Google Scholar 
[15] 
W. C. Troy, Solutions of thirdorder differential equations relevant to draining and coating flows, SIAM J. Math. Anal., 24 (1993), 155171. Google Scholar 
[16] 
E.O. Tuck and L.W. Schwartz, A boundary value problem from draining and coating flows involving a thirdorder differential equation relevant to draining and coating flows, SIAM Rev., 32 (1990), 453469. Google Scholar 
[17] 
B. Yan, D. O'Regan and R.P. Agarwal, Unbounded solutions for singular boundary value problems on the semiinfinite interval: Upper and lower solutions and multiplicity, J.Comput.Appl.Math., 197 (2006), 365386. Google Scholar 
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