Analysis of positive solutions to one-dimensional generalized double phase problems

We study positive solutions to the one-dimensional generalized double phase problems of the form: −(a(t)φp(u′)+b(t)φq(u′))′=λh(t)f(u),t∈(0,1),u(0)=0=u(1),\left\{\begin{array}{l}-(a\left(t){\varphi }_{p}\left(u^{\prime} )+b\left(t){\varphi }_{q}\left(u^{\prime} ))^{\prime} =\lambda h\left(t)f\left(u),\hspace{1em}t\in \left(0,1),\\ u\left(0)=0=u\left(1),\end{array}\right. where 1