Existence theorems for a second order nonlinear differential equation with nonlocal boundary conditions and their applications
Let \(w\in L^p(0,1)\) and \(\lambda\) be a parameter. The authors considered the second-order differential equation \[ \lambda u''(t)-w(t) f(t, u(t))=0 \] subject to one of the following sets of conditions: a. \(x(0)=x(1)=\int^1_0 g(t)x(t)\,dt\); b. \(x(0)=\int^1_0 g(t)x(t)\,dt\), \(x(1)=0\); c. \(x(0)=0\), \(x(1)=\int^1_0 g(t)x(t)\,dt\). By applying Hölder's inequality and fixed point theory in cones, they prove the existence and multiplicity of positive solutions of the above problems.
scientific article; zbMATH DE number 5728291
scientific article