Existence of nontrivial solutions to systems of multi-point boundary value problems Abstract References Full Text (368.8K)
John R. Graef - Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN 37403, United States (email) Abstract: In this paper, sufficient conditions are established for the existence of at least one nontrivial solution of the multi-point boundary value system $$ \left\{\begin{array}{ll} -(\phi_{p_i}(u'_{i}))'=\lambda F_{u_{i}}(x,u_{1},\ldots,u_{n}),\ x\in(0,1),\\ u_{i}(0)=\sum_{j=1}^m a_ju_i(x_j),\ u_{i}(1)=\sum_{j=1}^m b_ju_i(x_j), \end{array} \right. i=1,\ldots,n. $$ The approach is based on variational methods and critical point theory.
Keywords: Multi-point boundary value problem, critical point theory.
Received: July 2012; Revised: December 2012; Published: November 2013. |