On the eigenvalues of a non-linear Sturm-Liouville boundary value problem

چکیده مقاله

In the present paper‎, ‎a boundary value problem consisting of a non-linear Sturm-Liouville equation having a symmetric potential and a spectral parameter $\lambda$ with Dirichlet boundary conditions on the interval

‎$I:=(-1,1)$ is investigated‎. ‎For $1\leq q < \infty$‎, ‎we obtain the asymptotic formula for the $L^{q}$-bifurcation curve $\lambda=\lambda(q,\alpha)$ as $\alpha \rightarrow \infty$