scholarly journals Multiple solutions for the Dirichlet second-order boundary value problem of nonsingular type

1999 ◽  
Vol 37 (8) ◽  
pp. 99-106 ◽  
Author(s):  
R.P. Agarwal ◽  
D. O'Regan
Keyword(s):  
Boundary Value Problem ◽  
Multiple Solutions ◽  
Boundary Value ◽  
Second Order

scholarly journals Multiple solutions of boundary value problem

2006 ◽  
Vol 37 (2) ◽  
pp. 149-154
Author(s):  
Yongjin Li ◽  
Xiaobao Shu ◽  
Yuantong Xu
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Ordinary Differential Equations ◽  
Boundary Value Problems ◽  
Multiple Solutions ◽  
Boundary Value ◽  
Index Theory ◽  
Second Order ◽  
Group Index ◽  
Variational Structure

By means of variational structure and $ Z_2 $ group index theory, we obtain multiple solutions of boundary value problems for second-order ordinary differential equations$ \begin{cases} & - (ru')' + qu = \lambda f(t, u),\qquad 0 < t < 1 \\ & u'(0) = 0 = \gamma u(1)+ u'(1), \qquad \text{ where } \gamma \geq 0. \end{cases} $

scholarly journals Uniqueness and Multiplicity of Solutions for a Second-Order Discrete Boundary Value Problem with a Parameter

2008 ◽  
Vol 2008 ◽  
pp. 1-6
Author(s):  
Xi-Lan Liu ◽  
Jian-Hua Wu
Keyword(s):  
Difference Equation ◽  
Boundary Value Problem ◽  
Multiple Solutions ◽  
Boundary Value ◽  
Second Order ◽  
Order Difference ◽  
Multiplicity Of Solutions ◽  
Discrete Boundary Value Problem ◽  
Second Order Difference Equation ◽  
Order Difference Equation

This paper is concerned with the existence of unique and multiple solutions to the boundary value problem of a second-order difference equation with a parameter, which is a complement of the work by J. S. Yu and Z. M. Guo in 2006.

scholarly journals Existence of Multiple Solutions of a Second-Order Difference Boundary Value Problem

2010 ◽  
Vol 2010 ◽  
pp. 1-21 ◽  
Author(s):  
Bo Zheng ◽  
Huafeng Xiao
Keyword(s):  
Boundary Value Problem ◽  
Multiple Solutions ◽  
Mountain Pass Theorem ◽  
Boundary Value ◽  
Local Minimizer ◽  
Second Order ◽  
Critical Groups ◽  
Nontrivial Solutions ◽  
Difference Problem ◽  
Order Difference

This paper studies the existence of multiple solutions of the second-order difference boundary value problemΔ2u(n−1)+V′(u(n))=0,n∈ℤ(1,T),u(0)=0=u(T+1). By applying Morse theory, critical groups, and the mountain pass theorem, we prove that the previous equation has at least three nontrivial solutions when the problem is resonant at the eigenvalueλk  (k≥2)of linear difference problemΔ2u(n−1)+λu(n)=0,n∈ℤ(1,T),u(0)=0=u(T+1)near infinity and the trivial solution of the first equation is a local minimizer under some assumptions onV.

Existence of solutions for a second order boundary value problem with the Clarke subdifferential

Filomat ◽  
2017 ◽  
Vol 31 (9) ◽  
pp. 2763-2771 ◽  
Author(s):  
Dalila Azzam-Laouir ◽  
Samira Melit
Keyword(s):  
Boundary Value Problem ◽  
Differential Inclusion ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Second Order ◽  
Clarke Subdifferential ◽  
Lipschitzian Function ◽  
The Clarke Subdifferential

In this paper, we prove a theorem on the existence of solutions for a second order differential inclusion governed by the Clarke subdifferential of a Lipschitzian function and by a mixed semicontinuous perturbation.

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