Multiplicity of positive solutions for second-order differential inclusion systems depending on two parameters

Abstract

We consider the two-point boundary-value system $$\displaylines{ -u''_i+u_i\in\lambda\partial_{u_i}F(u_1,\ldots,u_n) +\mu\partial_{u_i}G(u_1,\ldots,u_n),\cr u'_i(a)=u'_i(b)=0\quad u_i\geq 0,\quad 1\leq i\leq n. }$$ Applying a version of nonsmooth three critical points theorem, we show the existence of at least three positive solutions.

Keywords

• Neumann problem
• differential inclusion system
• locally Lipschitz
• nonsmooth critical point