ON A THEORY BY SCHECHTER AND TINTAREV

Abstract

In this paper, we show that the beautiful theory developed by M. Schechter and K. Tintarev in [9] can be applied to the eigenvalue problem $$ \begin{cases} -\Delta u = \lambda f(u) & {\rm in} \,\,\, \Omega \\ u = 0 & {\rm on\,\, \partial} \Omega \end{cases} $$ when $$ \limsup_{|\xi|\to +\infty}{{\int_0^{\xi}f(t)dt}\over {\xi^2}}\lt +\infty$$ and, for each $\lambda$ in a suitable interval, the problem has a unique positive solution.