Prescribed energy solutions to some scaled problems via a scaled Nehari manifold

Kanishka Perera; Kaye Silva

Prescribed energy solutions to some scaled problems via a scaled Nehari manifold

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arxiv 2503.13648 v1 pith:B7UD4V2B submitted 2025-03-17 math.AP

Kanishka Perera , Kaye Silva This is my paper · ORCID

classification math.AP

keywords scaledenergymanifoldnehariprescribedproblemssolutionsapplications

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We prove the existence, multiplicity, and bifurcation of solutions with prescribed energy for a broad class of scaled problems by introducing a suitable notion of scaling based Nehari manifold. Applications are given to Schr\"{o}dinger--Poisson--Slater type equations.

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On the $N$-dimensional Schr\"{o}dinger--Poisson--Slater equation \`a la Brezis--Nirenberg
math.AP 2025-05 conditional novelty 6.0 of 10

For the N-dimensional Schrödinger-Poisson-Slater equation with critical exponent, the authors show existence and multiplicity of prescribed-energy radial solutions, including a sharp threshold case analysis.

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