Boundary value problems on [a,b) and singular perturbations
M. Cecchi, M. Marini, P. L. Zezza (1984)
Annales Polonici Mathematici
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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.
Yakovlev, M.N. (2004)
Zapiski Nauchnykh Seminarov POMI
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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...
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.
Kvinikadze, George (1998)
Memoirs on Differential Equations and Mathematical Physics
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Rudd, Matthew, Tisdell, Christopher C. (2009)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
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Zhou, W.S., Cai, S.F. (2006)
Lobachevskii Journal of Mathematics
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Lü, Haishen, O'Regan, Donal (2005)
Advances in Difference Equations [electronic only]
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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...
Eloe, Paul W., Henderson, Johnny (1995)
International Journal of Mathematics and Mathematical Sciences
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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...
Zhou, Wen-Shu (2007)
Applied Mathematics E-Notes [electronic only]
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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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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.