We show the existence of a nodal solution (sign‐changing solution) for a Kirchhoff equation of the type −M0true∫Ω|∇u|2dxΔu=f(u)inΩ,u=0on∂Ω,where Ω is a bounded domain in R3, M is a general C1 class function and f is a superlinear C1 class function with subcritical growth. The proof is based on a minimization argument and a quantitative deformation lemma.

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Using variational methods we establish existence and concentration of positive solutions for a class of elliptic problems in $\mathbf{R}^{N}$, whose nonlinearity is discontinuous.