Multibump nodal solutions for an indefinite nonhomogeneous elliptic problem

Abstract

We construct multibump nodal solutions of the elliptic equation $$ -\Delta u=a^+[\lambda u+ f(\, \cdot\,, u)]-\mu a^- g(\, \cdot\,, u) $$ in $H^1_0(\Omega)$, when $\mu$ is large, under appropriate assumptions, for $f$ superlinear and subcritical and such that the eigenvalues of the associated linearized operator on $H^1_0(\{x\in\Omega:\: a(x)>0\})$ at zero, $u\longmapsto u-\lambda(-\Delta)^{-1}(a^+ u)$, are positive. The solutions are of least energy in some Nehari-type set defined by imposing suitable conditions on orthogonal components of functions in $H^1_0(\Omega)$.