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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Jesús M. F. Castillo, Marilda Simoes, Jesús Suárez de la Fuente (2012)
Bulletin of the Polish Academy of Sciences. Mathematics
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We exhibit new examples of weakly compact strictly singular operators with dual not strictly cosingular and characterize the weakly compact strictly singular surjections with strictly cosingular adjoint as those having strictly singular bitranspose. We then obtain new examples of super-strictly singular quotient maps and show that the strictly singular quotient maps in Kalton-Peck sequences are not super-strictly singular.
M. Cecchi, M. Marini, P. L. Zezza (1984)
Annales Polonici Mathematici
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Daqing Jiang (2000)
Annales Polonici Mathematici
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We study the existence of positive solutions to the singular boundary value problem for a second-order FDE ⎧ u'' + q(t) f(t,u(w(t))) = 0, for almost all 0 < t < 1, ⎨ u(t) = ξ(t), a ≤ t ≤ 0, ⎩ u(t) = η(t), 1 ≤ t ≤ b, where q(t) may be singular at t = 0 and t = 1, f(t,u) may be superlinear at u = ∞ and singular at u = 0.
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.
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...
Miroljub Jevtić (1983)
Publications de l'Institut Mathématique
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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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Rudd, Matthew, Tisdell, Christopher C. (2009)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
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Joe Howard (1970)
Colloquium Mathematicae
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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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Zhou, W.S., Cai, S.F. (2006)
Lobachevskii Journal of Mathematics
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Masatomo Takahashi (2007)
Colloquium Mathematicae
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A complete solution of an implicit second order ordinary differential equation is defined by an immersive two-parameter family of geometric solutions on the equation hypersurface. We show that a completely integrable equation is either of Clairaut type or of first order type. Moreover, we define a complete singular solution, an immersive one-parameter family of singular solutions on the contact singular set. We give conditions for existence of a complete solution and a complete singular...
Rabtsevich, V.A. (2000)
Memoirs on Differential Equations and Mathematical Physics
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Rabtsevich, V.A. (2000)
Memoirs on Differential Equations and Mathematical Physics
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