arXiv subjects
Publications and source records attributed to José Maria Gomes.
We define some Nehari-type constraints using an orthogonal decomposition of the Sobolev space $H^1_0$ and prove the existence of multibump nodal solutions for an indefinite superlinear elliptic problem.
We construct multibump nodal solutions of the elliptic equation $$ -Δu=a^+[λu+ f(\, \cdot\,, u)]-μa^- g(\, \cdot\,, u) $$ in $H^1_0(Ω)$, when $μ$ is large, under appropriate assumptions, for $f$ superlinear and subcritical and such that the eigenvalues of the associated linearized operator on $H^1_0(\{x\inΩ:\: a(x)>0\})$ at zero, $u\longmapsto u-λ(-Δ)^{-1}(a^+ u)$, are positive. The solutions are of least energy in some Nehari-type set defined by imposing suitable conditions on orthogonal components of functions in $H^1_0(Ω)$.