%0 Journal Article
%T Infinitely many solutions to superlinear second order m-point boundary value problems
%A Ma Ruyun
%A Gao Chenghua
%A Chen Xiaoqiang
%J Boundary Value Problems
%D 2011
%I Springer
%X We consider the boundary value problem u ¡å ( x ) + g ( u ( x ) ) + p ( x , u ( x ) , u ¡ä ( x ) ) = 0 , x ¡Ê ( 0 , 1 ) , u ( 0 ) = 0 , u ( 1 ) = ¡Æ i = 1 m - 2 ¦Á i u ( ¦Ç i ) , where: (1) m ¡Ý 3, ¦Çi ¡Ê (0, 1) and ¦Ái > 0 with A : = ¡Æ i = 1 m - 2 ¦Á i < 1 ; (2) g :   ¡ú   is continuous and satisfies g ( s ) s > 0 , s ¡Ù 0 , and lim s ¡ú ¡Þ g ( s ) s = ¡Þ ; (3) p : [0, 1] ¡Á  2 ¡ú   is continuous and satisfies | p ( x , u , v ) | ¡Ü C + ¦Â | u | , x ¡Ê [ 0 , 1 ] ( u , v ) ¡Ê   2 for some C > 0 and ¦Â ¡Ê (0, 1/2). We obtain infinitely many solutions having specified nodal properties by the bifurcation techniques. MSC(2000). 34B15, 58E05, 47J10
%K Nodal solutions
%K Second order equations
%K Multi-point boundary value problems
%K Bifurcation
%U http://www.boundaryvalueproblems.com/content/2011/1/14