Multiplicity of positive solutions for a nonlinear fourth order equation

Volume 77 / 2001

D. R. Dunninger Annales Polonici Mathematici 77 (2001), 161-168 MSC: Primary 34B18. DOI: 10.4064/ap77-2-3


We study the existence and multiplicity of positive solutions of the nonlinear fourth order problem $$ \left\{\eqalign{&\!u^{(4)} =\lambda f(u) \quad \hbox{in } (0,1),\cr &\!u(0)=a\ge 0, \quad u'(0)=a'\ge 0,\quad u(1)=b\ge 0,\quad u'(1)=-b'\le 0.\cr}\right. $$ The methods employed are upper and lower solutions and degree theory arguments.


  • D. R. DunningerDepartment of Mathematics
    Michigan State University
    East Lansing, MI 48824, U.S.A.

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