Existence of positive solutions of fourth-order problems with integral boundary conditions.
Ma, Ruyun, Chen, Tianlan (2011)
Boundary Value Problems [electronic only]
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Ma, Ruyun, Chen, Tianlan (2011)
Boundary Value Problems [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.
Jan Ligęza (2005)
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
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We study the existence of positive solutions of the integral equation in both and spaces, where and . Throughout this paper is nonnegative but the nonlinearity may take negative values. The Krasnosielski fixed point theorem on cone is used.
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.
Jong Yeoul Park, Jeong Ja Bae (2000)
Czechoslovak Mathematical Journal
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In this paper we consider the existence and asymptotic behavior of solutions of the following problem: where , , , , , and is the Laplacian in .