Positive solutions for nonlocal differential equations with concave and convex coefficients (Q6624927)

In this paper the authors study the positive solutions for nonlocal differential equations with concave and convex coefficients \N\[\N-A\left(\int_0^1(u^p(s)+u^q(s))\mathrm{d}s\right)u''(t)=f(t,u(t)),\quad t\in(0,1), \N\]\Nwhere the function \(A:\mathbb{R}\to\mathbb{R}\) is continuous, \(0<p<1\leq q\), the nonlinear term \(f(t,x)\) is continuous, has a singularity at \(x=0\) and changes sign. The authors obtained the existence and multiplicity results of above problem by using the fixed point index theory and fixed point theorems on cones.