Existence of nonnegative solutions of singular boundary-value problems for second-order ordinary differential equations.
Yakovlev, M.N. (2005)
Zapiski Nauchnykh Seminarov POMI
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Yakovlev, M.N. (2005)
Zapiski Nauchnykh Seminarov POMI
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Qingliu Yao (2013)
Annales Polonici Mathematici
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We study the existence of positive solutions to a class of singular nonlinear fourth-order boundary value problems in which the nonlinearity may lack homogeneity. By introducing suitable control functions and applying cone expansion and cone compression, we prove three existence theorems. Our main results improve the existence result in [Z. L. Wei, Appl. Math. Comput. 153 (2004), 865-884] where the nonlinearity has a certain homogeneity.
M. Cecchi, M. Marini, P. L. Zezza (1984)
Annales Polonici Mathematici
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Rudd, Matthew, Tisdell, Christopher C. (2009)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
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Qingliu Yao (2011)
Annales Polonici Mathematici
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This paper studies the existence of multiple positive solutions to a nonlinear fourth-order two-point boundary value problem, where the nonlinear term may be singular with respect to both time and space variables. In order to estimate the growth of the nonlinear term, we introduce new control functions. By applying the Hammerstein integral equation and the Guo-Krasnosel'skii fixed point theorem of cone expansion-compression type, several local existence theorems are proved.
Eloe, Paul W., Henderson, Johnny (1995)
International Journal of Mathematics and Mathematical Sciences
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Zhou, Wen-Shu (2007)
Applied Mathematics E-Notes [electronic only]
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Lü, Haishen, O'Regan, Donal (2005)
Advances in Difference Equations [electronic only]
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Gabriele Bonanno (1996)
Annales Polonici Mathematici
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Existence theorems of positive solutions to a class of singular second order boundary value problems of the form y'' + f(x,y,y') = 0, 0 < x < 1, are established. It is not required that the function (x,y,z) → f(x,y,z) be nonincreasing in y and/or z, as is generally assumed. However, when (x,y,z) → f(x,y,z) is nonincreasing in y and z, some of O'Regan's results [J. Differential Equations 84 (1990), 228-251] are improved. The proofs of the main theorems are based on a fixed point...
Jiang, Daqing, Zhang, Lili, O&#039;Regan, Donal, Agarwal, Ravi P. (2003)
Journal of Applied Mathematics and Stochastic Analysis
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Lin, Xiaoning, Sun, Weizhi, Jiang, Daqing (2008)
Boundary Value Problems [electronic only]
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Daqing Jiang, Xiaojie Xu, Donal O&#039;Regan, Ravi P. Agarwal (2003)
Annales Polonici Mathematici
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The existence of single and multiple nonnegative solutions for singular positone boundary value problems to the delay one-dimensional p-Laplacian is discussed. Throughout our nonlinearity f(·,y) may be singular at y = 0.
E. M. Rojas
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We study the solvability and Fredholmness of binomial boundary value problems for analytic functions represented by integrals of Cauchy type with density on abstract nonstandard Banach function spaces, assuming continuous, piecewise continuous and essentially bounded factorizable functions as coefficients. The representation of the solutions of those problems allows us to describe the explicit form of the solutions of the associated singular integral equations in each case. The solvability...
Kvinikadze, George (1998)
Memoirs on Differential Equations and Mathematical Physics
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Yakovlev, M.N. (2004)
Zapiski Nauchnykh Seminarov POMI
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Li, Xiuying, Wu, Boying (2011)
Bulletin of the Malaysian Mathematical Sciences Society. Second Series
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Yuan, Chengjun, Jiang, Daqing, Zhang, You (2008)
Boundary Value Problems [electronic only]
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