Three positive radial solutions for elliptic equations in a ball

In this work we deal with a class of second-order elliptic problems of the form $-\Delta u=\lambda k\left(\left|x\right|\right)f\left(u\right)\text{ in }\Omega$, with non-homogeneous boundary condition $u=a\text{ on }\partial \Omega$ where $\Omega$ is the ball of radius $R_0$ centered at origin, $\lambda ,a$ are positive parameters, $f\in C([0,+\infty ),[0,+\infty ))$ is an increasing function and $k\in C([0,R_0],[0,+\infty ))$ is not identically zero on any subinterval of $[0,R_0]$. We obtain via a fixed point theorem of cone expansion/compression type the existence of at least three positive radial solutions.