Positive solutions of higher-order four-point boundary value problem with \(p\)-Laplacian operator
The authors consider the existence of positive solutions for a four-point singular boundary value problem of the form \[ \begin{aligned} &(\phi_p(u^{(n-1)}(t)))'+a(t)f(u(t),u'(t),\dots,u^{(n-1)}(t))=0,\quad t\in(0,1),\\ &u^{(i)}(0)=0,\quad 0\leq i\leq n-3,\\ &\lambda_1\phi_p(u^{(n-2)}(0))-\mu_1\phi_p(u^{(n-1)}(\xi))=0,\\ &\lambda_2\phi_p(u^{(n-2)}(1))+\mu_2\phi_p(u^{(n-1)}(\eta))=0, \end{aligned} \] where \(\phi_p(s)=|s|^{p-2}s,\;p>1\). By means of the fixed point theorem due to Bai and Ge, some sufficient conditions for the existence of positive solutions are presented.
four-point singular boundary value problem
scientific article; zbMATH DE number 5677323