Some applications of the Nehari manifold method to functionals in $C^1(X \setminus \{0\})$

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发表日期：

2025年1月6日

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Edir Júnior Ferreira Leite,
Humberto Ramos Quoirin,
Kaye Silva

摘要

Given a real Banach space X, we show that the Nehari manifold method can be applied to functionals which are $C^1$ $C^{1}$ in $X {\setminus } \{0\}$ $X \ {0}$ . In particular we deal with functionals that can be unbounded near 0, and prove the existence of a ground state and infinitely many critical points for such functionals. These results are then applied to three classes of problems: the prescribed energy problem for a family of functionals depending on a parameter, problems involving the affine p-Laplacian operator, and degenerate Kirchhoff type problems.

Some applications of the Nehari manifold method to functionals in \(C^1(X \setminus \{0\})\)

摘要