Triple positive solutions for system of nonlinear second-order three point boundary value problem
The paper concerns the system of second-order differential equations on \([0,1]\): NEWLINE\[NEWLINE \begin{aligned} &u''+k^2u=f(t,u,v),\quad 0<t<1,\\ &v''+k^2v=g(t,u,v),\quad 0<t<1,\\ &u(0)=u'(0)=0,\\ &u(1)=\beta u(\eta),\;v(1)=\lambda v(\eta), \end{aligned} NEWLINE\]NEWLINE where \(f, g: [0,1]\times[0,\infty)\times[0,\infty)\longrightarrow [0,\infty)\) are continuous functions, \(0<\eta<1\), \(0<\beta<\beta_0\) and \(0<\lambda<\lambda_0\) for some \(\beta_0, \lambda_0\). Under some local growth conditions on the nonlinearities, the existence of three nonegative solutions is proved using the classical Legget-Williams fixed point theorem.
scientific article; zbMATH DE number 6229334