New results on the positive solutions of nonlinear second-order differential systems.
Guo, Yingxin (2009)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
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Guo, Yingxin (2009)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
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Qingliu Yao (2013)
Applications of Mathematics
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We consider the classical nonlinear fourth-order two-point boundary value problem In this problem, the nonlinear term contains the first and second derivatives of the unknown function, and the function may be singular at , and at , , . By introducing suitable height functions and applying the fixed point theorem on the cone, we establish several local existence theorems on positive solutions and obtain the corresponding eigenvalue intervals.
Staněk, Svatoslav (2002)
Archivum Mathematicum
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We consider boundary value problems for second order differential equations of the form with the boundary conditions , , where are continuous functions, satisfies the local Carathéodory conditions and are continuous and nondecreasing functionals. Existence results are proved by the method of lower and upper functions and applying the degree theory for -condensing operators.
Chunmei Miao, Junfang Zhao, Weigao Ge (2009)
Czechoslovak Mathematical Journal
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In this paper we deal with the four-point singular boundary value problem where , , , , , , , and may be singular at . By using the well-known theory of the Leray-Schauder degree, sufficient conditions are given for the existence of positive solutions.
Georgiev, Svetlin Georgiev (2007)
Boundary Value Problems [electronic only]
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Svatoslav Staněk (1995)
Annales Polonici Mathematici
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The differential equation of the form , a ∈ (0,∞), is considered and solutions u with u(0) = 0 and (u(t))² + (u’(t))² > 0 on (0,∞) are studied. Theorems about existence, uniqueness, boundedness and dependence of solutions on a parameter are given.