2 problems

Consider the second-order boundary-value problem … with … where $K$ and $A$ are positive constants and $L(x)=a_0^2+(a_1^2-a_0^2)x$, with $a_0,a_1>0$. Exact multiplicity conjecture.…

Let $F$ be the operator in problem, with principal half-eigenvalues $\lambda_1^+(F)$ and $\lambda_1^-(F)$, and let $f$ be the datum in that problem. Multiplicity conjecture. There…