Half-eigenvalues of self-adjoint, $2m$th-order differential operators and semilinear problems with jumping nonlinearities
Half-eigenvalues of self-adjoint, $2m$th-order differential operators and semilinear problems with jumping nonlinearities
We consider semilinear boundary value problems of the form \begin{equation} L u(x) = f(x,u(x)) + h(x), \quad x \in (0,\pi), \tag*{(1)} \end{equation} where $L$ is a $2m$th-order, self-adjoint, disconjugate ordinary differential operator on $[0,\pi]$, together with appropriate boundary conditions at $0$ and $\pi$, while $f : [0,\pi] {\times} \mathbb R …