A singular eigenvalue problem for second order linear ordinary differential equations.
Takaŝi, Kusano, Naito, Manabu (1997)
Memoirs on Differential Equations and Mathematical Physics
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Takaŝi, Kusano, Naito, Manabu (1997)
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.
Martínez, Sandra, Rossi, Julio D. (2002)
Abstract and Applied Analysis
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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.
Denny, Cathryn, Hankerson, Darrel (1993)
International Journal of Mathematics and Mathematical Sciences
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Eberhard, W., Freiling, G., Schneider, A. (1992)
International Journal of Mathematics and Mathematical Sciences
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Dai, Xiaoying, He, Lianhua, Zhou, Aihui
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We review some numerical analysis of an adaptive finite element method (AFEM) for a class of elliptic partial differential equations based on a perturbation argument. This argument makes use of the relationship between the general problem and a model problem, whose adaptive finite element analysis is existing, from which we get the convergence and the complexity of adaptive finite element methods for a nonsymmetric boundary value problem, an eigenvalue problem, a nonlinear boundary...
Yakovlev, M.N. (2005)
Zapiski Nauchnykh Seminarov POMI
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Eloe, Paul W., Henderson, Johnny (1995)
International Journal of Mathematics and Mathematical Sciences
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Henderson, Johnny, Lauer, Susan D. (1997)
Abstract and Applied Analysis
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Julián Fernández Bonder, Julio D. Rossi (2002)
Publicacions Matemàtiques
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In this paper we study the Sobolev trace embedding W(Ω) → L (∂Ω), where V is an indefinite weight. This embedding leads to a nonlinear eigenvalue problem where the eigenvalue appears at the (nonlinear) boundary condition. We prove that there exists a sequence of variational eigenvalues λ / +∞ and then show that the first eigenvalue is isolated, simple and monotone with respect to the weight. Then we prove a nonexistence result related to the first eigenvalue and we end...
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.
Albert Schneider (1974)
Mathematische Zeitschrift
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Lin, Xiaoning, Sun, Weizhi, Jiang, Daqing (2008)
Boundary Value Problems [electronic only]
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