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 $H_0^1(\Omega )$, when $\mu$ is large, under appropriate assumptions, for $f$ superlinear and subcritical and such that the eigenvalues of the associated linearized operator on $H_0^1(\{x\in \Omega :a(x)>0\})$ at zero, $u⟼u-\lambda (-\Delta {)}^{-1}(a^{+}u)$, are positive. The solutions are of least energy in some Nehari-type set defined by imposing suitable conditions on orthogonal components of functions in $H_0^1(\Omega )$.