Positive solutions for nonlocal differential equations with concave and convex coefficients
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.
scientific article; zbMATH DE number 7932489
scientific article