Abstract In this article, we study the existence of ground state solutions for Schrödinger-Poisson-Slater type equation with Coulomb-Sobolev critical growth: − Δ u + 1 4</m:mn...

Let (M,g,σ) be a compact Riemannian spin manifold of dimension m≥2, let S(M) denote the spinor bundle on M, and D Atiyah-Singer Dirac operator acting spinors ψ:M→S(M). We study existence solutions nonlinear equation with critical exponent(NLD)Dψ=λψ+f(|ψ|)ψ+|ψ|2m−1ψ where λ∈R f(|ψ|)ψ is subcritical nonlinearity in sense that f(s)=o(s2m−1) as s→∞. A model f(s)=αsp−2 2<p<2mm−1, α∈R. In particular ...

Given a smooth compact Riemannian n–manifold (M, g), we consider the equation ∆gu+ hu = |u| ∗−2−ε u, where h is a C–function on M , the exponent 2∗ := 2n/ (n− 2) is the critical Sobolev exponent, and ε is a small positive real parameter such that ε→ 0. We prove the existence of blowing-up families of sign-changing solutions which develop bubble towers at some point where the function h is great...

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