Abstract
We investigate zero energy critical points for a class of functionals $\Phi_\mu$ defined on a uniformly convex Banach space, and depending on a real parameter $\mu$. More precisely, we show the existence of a sequence $(\mu_n)$ such that $\Phi_{\mu_n}$ has a pair of critical points $\pm u_n$ satisfying $\Phi_{\mu_n}(\pm u_n)=0$, for every $n$. In addition, we provide some properties of $\mu_n$ and $u_n$. This result, which is proved by combining the nonlinear generalized Rayleigh quotient method [10] with the Ljusternik-Schnirelman theory, is then applied to several classes of elliptic pdes.
Citation
Humberto Ramos Quoirin. Jefferson Silva. Kaye Silva. "Zero energy critical points of functionals depending on a parameter." Differential Integral Equations 36 (5/6) 413 - 436, May/June 2023. https://doi.org/10.57262/die036-0506-413
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