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Note on elliptic equations on closed manifolds with singular nonlinearities
Published 30 Apr 2025 in math.AP | (2504.21339v1)
Abstract: We consider a general elliptic equation $$ -\Delta_g u+V(x)u=f(x,u)+g(x,u2)u $$ on a closed Riemannian manifold $(M, g)$ and utilize a recent variational approach by Hebey, Pacard, Pollack to show the existence of a nontrivial solution under general assumptions on nonlinear terms $f$ and $g$.
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