Homogenization of Fucik eigenvalues by optimal partition methods

Abstract

Given a bounded domain $\Omega$ in ${\mathbb{R}}^N$, $N\ge 1$ we study the asymptotic behavior as $\epsilon \to 0$ of the eigencurves of $$-{\Delta }_p{u}_{\epsilon }={\alpha }_{\epsilon }m(\frac{x}{\epsilon })(u_{\epsilon }^{+}{)}^{p-1}-{\beta }_{\epsilon }n(\frac{x}{\epsilon })(u_{\epsilon }^{-}{)}^{p-1}\text{ in }\Omega$$ with Dirichlet boundary conditions, where $m$ and $n$ are bounded periodic weights. In this work we obtain accurate bounds of the convergence rates of these curves to some limit curves as $\epsilon \to 0$.

13 pages

References in corpus (1)

• Quasilinear eigenvalues