TY  - JOUR
ID  - Graef2013
LB  - Graef2013
AU  - Graef, John R.
AU  - Heidarkhani, Shapour
AU  - Kong, Lingju
TI  - Multiple solutions for systems of multi-point boundary value problems
ST  - Multiple solutions for systems of multi-point boundary value problems
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2013
VL  - 33
IS  - 2
SP  - 293
EP  - 306
DO  - http://dx.doi.org/10.7494/OpMath.2013.33.2.293
UR  - http://dx.doi.org/10.7494/OpMath.2013.33.2.293
AB  - In this paper, we establish the existence of at least three solutions of the multi-point boundary value system \[\left\{\begin{array}{ll} -(\phi_{p_i}(u'_{i}))'=\lambda F_{u_{i}}(x,u_{1},\ldots,u_{n}),\ t\in(0,1),\\ u_{i}(0)=\sum_{j=1}^m a_ju_i(x_j),\ u_{i}(1)=\sum_{j=1}^m b_ju_i(x_j), \end{array}\right. i=1,\ldots,n.\] The approaches used are based on variational methods and critical point theory.
KW  - multiple solutions
KW  - multi-point boundary value problem
KW  - critical point theory
SN  - 1232-9274
ER  -