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  1. 4 Annales Polonici Mathematici

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  1. 4 Yao Q.

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  1. 1 2013

  2. 2 2011

  3. 1 2010

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Positive solutions and eigenvalue intervals of a singular third-order boundary value problem

100%
Yao Q.
Annales Polonici Mathematici
|
2011
|
tom 102
|
nr 1
25-37
EN
This paper studies positive solutions and eigenvalue intervals of a nonlinear third-order two-point boundary value problem. The nonlinear term is allowed to be singular with respect to both the time and space variables. By constructing a proper cone and applying the Guo-Krasnosel'skii fixed point theorem, the eigenvalue intervals for which there exist one, two, three or infinitely many positive solutions are obtained.
2
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Positive solutions to a singular fourth-order two-point boundary value problem

100%
Yao Q.
Annales Polonici Mathematici
|
2011
|
tom 100
|
nr 1
1-12
EN
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.
3
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A class of singular fourth-order boundary value problems with nonhomogeneous nonlinearity

100%
Yao Q.
Annales Polonici Mathematici
|
2013
|
tom 109
|
nr 3
311-325
EN
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.
4
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Positive solutions to a class of elastic beam equations with semipositone nonlinearity

100%
Yao Q.
Annales Polonici Mathematici
|
2010
|
tom 97
|
nr 1
35-50
EN
Let h ∈ L¹[0,1] ∩ C(0,1) be nonnegative and f(t,u,v) + h(t) ≥ 0. We study the existence and multiplicity of positive solutions for the nonlinear fourth-order two-point boundary value problem $u^{(4)}(t) = f(t,u(t),u'(t))$, 0 < t < 1, u(0) = u'(0) = u'(1) =u'''(1) =0, where the nonlinear term f(t,u,v) may be singular at t=0 and t=1. By constructing a suitable cone and integrating certain height functions of f(t,u,v) on some bounded sets, several new results are obtained. In mechanics, the problem models the deflection of an elastic beam fixed at the left end and clamped at the right end by sliding clamps.
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