Positive solutions of boundary-value problems for disfocal ordinary differential equations
The paper is concerned with finding values of \(\lambda\in(0,\infty)\) for which there exist positive solutions to the boundary value problem \[ Lx(t)+ \lambda a(t)f(x(t))= 0,\quad t\in[0,1],\quad x(0)= x(1)= 0, \] where \(Lx(t)= 0\), \(0\leq t\leq 1\) denotes a disfocal second-order ordinary differential equation, \(f:[0,+\infty)\to [0,+\infty)\) and \(a: [0,1]\to [0,+\infty)\) are continuous functions. The author applies a cone-theoretic fixed point theorem to prove the existence of positive solutions and multiple positive solutions.
disfocal second-order ordinary differential equation
scientific article; zbMATH DE number 1135863