Access the full text.
Sign up today, get DeepDyve free for 14 days.
Bing Liu (2004)
Positive solutions of three-point boundary value problems for the one-dimensional p-laplacian with infinitely many singularitiesAppl. Math. Lett., 17
P. Wong, R. Agarwal (1998)
On eigenvalue intervals and twin eigenfunctions of higher-order boundary value problemsJournal of Computational and Applied Mathematics, 88
Zhilin Yang, Liang-Qian Kong (2012)
Positive solutions of a system of second order boundary value problems involving first order derivatives via R+n-monotone matricesNonlinear Analysis-theory Methods & Applications, 75
S. Djebali, K. Mebarki (2009)
Existence and multiplicity results for singular φ-laplacian BVPS on the positive half-line
J. Webb (2009)
Nonlocal conjugate type boundary value problems of higher orderNonlinear Analysis-theory Methods & Applications, 71
Kamal Bachouche, S. Djebali, T. Moussaoui (2012)
φ-LAPLACIAN BVPS WITH LINEAR BOUNDED OPERATOR CONDITIONS
Yonghong Ding (2011)
Positive Solutions for Integral Boundary Value Problem with ϕ-Laplacian OperatorBoundary Value Problems, 2011
J. Fialho, F. Minhós (2012)
On higher order fully periodic boundary value problemsJournal of Mathematical Analysis and Applications, 395
C Pang, W Dong, Z Wei (2006)
Greens function and positive solutions of $$n$$ n th order $$m$$ m -point boundary value problemAppl. Math. Comput., 182
A Benmezai, S Djebali, T Moussaoui (2008)
Existence results for one-dimensional Dirichlet $$\phi $$ ϕ -Laplacian BVPs: a fixed point approachDyn. Syst. Appl., 17
Zhiyong Wang, Jihui Zhang (2006)
Positive solutions for one-dimensional p-Laplacian boundary value problems with dependence on the first order derivativeJournal of Mathematical Analysis and Applications, 314
B Liu (2004)
Positive solutions of three-point boundary value problems for the one-dimensional $$p$$ p -Laplacian with infinitely many singularitiesAppl. Math. Lett., 17
J. Graef, L. Kong, F. Minhós (2011)
Higher order boundary value problems with phi-Laplacian and functional boundary conditionsComput. Math. Appl., 61
Junyu Wang (1997)
The existence of positive solutions for the one-dimensional $p$-Laplacian, 125
Dehong Ji, W. Ge (2007)
Multiple positive solutions for some p-Laplacian boundary value problemsAppl. Math. Comput., 187
K Bachouche, S Djebali, T Moussaoui (2011)
One-dimensional Dirichlet $$\phi $$ ϕ -Laplacian BVPs with first order derivative dependenceAdv. Dyn. Syst. Appl., 6
M. Krein, M. Rutman (1950)
Linear operators leaving invariant a cone in a Banach space, 10
Z Yang, D O’Regan (2012)
Positive solutions of a focal problem for one-dimensional $$p$$ p -Laplacian equationsMath. Comput. Model., 55
Changci Pang, Weisong Dong, Zhongli Wei (2006)
Green's function and positive solutions of nth order m-point boundary value problemAppl. Math. Comput., 182
T. Moussaoui, El-Alia Bab-ezouar (2008)
EXISTENCE RESULTS FOR ONE-DIMENSIONAL DIRICHLET -LAPLACIAN BVPS: A FIXED POINT APPROACH
Kamal Bachouche, S. Djebali, T. Moussaoui (2012)
$\phi$-Laplacian BVPs with linear bounded operator conditions, 48
Weihua Jiang (2008)
Multiple positive solutions for nth-order m-point boundary value problems with all derivativesNonlinear Analysis-theory Methods & Applications, 68
Zhilin Yang, D. O’Regan (2012)
Positive solutions of a focal problem for one-dimensional p-Laplacian equationsMath. Comput. Model., 55
L. Kong, Qingkai Kong (2010)
Higher order boundary value problems with nonhomogeneous boundary conditionsNonlinear Analysis-theory Methods & Applications, 72
(2009)
Solvability of the φ-Laplacian with nonlocal boundary conditions
B Yang (2010)
Positive solutions of the $$(n-1,1)$$ ( n - 1 , 1 ) conjugate boundary value problemElectron. J. Qual. Theory Differ. Equ., 53
K. Bachouche, Doudou Ben-Aknoun, S. Djebali, T. Moussaoui (2011)
One-Dimensional Dirichlet -Laplacian BVPs with First-Order Derivative Dependence
W Jiang (2008)
Multiple positive solutions for $$n$$ n th-order $$m$$ m -point boundary value problems with all derivativesNonlinear Anal., 68
Zhilin Yang (2011)
Positive solutions for a system of p-Laplacian boundary value problemsComput. Math. Appl., 62
Z Yang, L Kong (2012)
Positive solutions of a system of second order boundary value problems involving first order derivatives via $$\mathbb{R}_+^n$$ R + n -monotone matricesNonlinear Anal., 75
Ruyun Ma (2000)
Positive Solutions for Semipositone (k, n − k) Conjugate Boundary Value Problems☆☆☆Journal of Mathematical Analysis and Applications, 252
Z Yang (2011)
Positive solutions for a system of $$p$$ p -Laplacian boundary value problemsComput. Math. Appl., 62
D. Guo, W. Ames, Lakshmikantham (1988)
Nonlinear problems in abstract cones
J Wang (1997)
The existence of positive solutions for the one-dimensional $$p$$ p -LaplacianProc. Am. Math. Soc., 125
GL Karakostas (2004)
Triple positive solutions for the $$\Phi $$ Φ -Laplacian when $$\Phi $$ Φ is a sup-multiplicative-like functionElectron. J. Differ. Equ., 69
Yude Ji, Yanping Guo (2009)
The existence of countably many positive solutions for some nonlinear nth order m-point boundary value problemsJ. Comput. Appl. Math., 232
S. Djebali, O. Saifi (2009)
Positive solutions for singular $\phi-$Laplacian BVPs on the positive half-lineElectronic Journal of Qualitative Theory of Differential Equations
GL Karakostas (2009)
Solvability of the $$\phi $$ ϕ -Laplacian with nonlocal boundary conditionsAppl. Math. Comput., 215
H Feng, W Ge, M Jiang (2008)
Multiple positive solutions for m-point boundary-value problems with a one-dimensional $$p$$ p -LaplacianNonlinear Anal., 68
R Ma (2000)
Positive solutions for semipositone $$(k, n-k)$$ ( k , n - k ) conjugate boundary value problemsJ. Math. Anal. Appl., 252
John Davis, P. Eloe, J. Henderson (1999)
Triple positive solutions and dependence on higher order derivativesJournal of Mathematical Analysis and Applications, 237
G. Karakostas (2004)
Triple positive solutions for the -Laplacian when is a sup-multiplicative-like function.Electronic Journal of Differential Equations, 2004
Bo Yang (2010)
Positive solutions of the conjugate boundary value problem., 2010
Bo Yang (2010)
Positive Solutions of the (n-1, 1) Conjugate Boundary Value ProblemElectronic Journal of Qualitative Theory of Differential Equations, 2010
D. Jiang (2000)
Multiple positive solutions to singular boundary value problems for superlinear higher-order ODEs☆Computers & Mathematics With Applications, 40
Y Ji, Y Guo (2009)
The existence of countably many positive solutions for some nonlinear $$n$$ n th order $$m$$ m -point boundary value problemsJ. Comput. Appl. Math., 232
H. Feng, W. Ge, Ming Jiang (2008)
Multiple positive solutions for m-point boundary-value problems with a one-dimensional p-LaplacianNonlinear Analysis-theory Methods & Applications, 68
Junyuan Yang, Xiaoyan Wang (2010)
Existence of a Nonautonomous SIR Epidemic Model with Age StructureAdvances in Difference Equations, 2010
K Bachouche, S Djebali, T Moussaoui (2012)
$$\phi $$ ϕ -Laplacian BVPs with linear bounded operator conditionsArch. Math. (Brno), 48
This paper is concerned with the existence and multiplicity of positive solutions of the $$n$$ n th-order quasilinear boundary value problem $$\begin{aligned} {\left\{ \begin{array}{ll} -(\varphi (u^{(n-1)}))^\prime =f(t,u), \quad \text {a.e.}\ t\in [0,1],\\ u^{(i)}(0) = u^{(n-1)}(1)=0\ \quad (i=0, \ldots , n-2), \end{array}\right. } \end{aligned}$$ - ( φ ( u ( n - 1 ) ) ) ′ = f ( t , u ) , a.e. t ∈ [ 0 , 1 ] , u ( i ) ( 0 ) = u ( n - 1 ) ( 1 ) = 0 ( i = 0 , … , n - 2 ) , where $$n\geqslant 2$$ n ⩾ 2 , $$\varphi : \mathbb R^+\rightarrow \mathbb R^+$$ φ : R + → R + is either a convex or concave homeomorphism, and $$f\in C([0,1]\times \mathbb R^+,\mathbb R^+)(\mathbb R^+:=[0,\infty ))$$ f ∈ C ( [ 0 , 1 ] × R + , R + ) ( R + : = [ 0 , ∞ ) ) . Based on a priori estimates achieved by utilizing Jensen’s inequalities for concave and convex functions, we use fixed point index theory to establish our main results.
Positivity – Springer Journals
Published: Mar 4, 2014
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.