The existence of positive solutions for some nonlinear equation systems
The authors consider the existence of positive solutions of the following boundary value problem: \[ \begin{cases} (\phi_1(x'))'+a(t)f(x,y)=0,&(\phi_2(y'))'+b(t)g(x,y)=0,\quad t\in(0,1),\\ \alpha\phi_1(x(0))-\beta\phi_1(x'(0))=0,&\alpha\phi_2(y(0))-\beta\phi_2(y'(0))=0,\\ \gamma\phi_1(x(1))+\mu\phi_1(x'(1))=0,&\gamma\phi_2(y(1))+\mu\phi_2(y'(1))=0, \end{cases} \] where \(\phi_1,\phi_2:\mathbb R\to\mathbb R\) are homeomorphisms and \(\phi_1(0)=0,\) \(\phi_2(0)=0\). They present sufficient conditions for the existence of positive solutions by using a fixed-point theorem.
scientific article; zbMATH DE number 5072998