Electronic Journal of Differential Equations, Vol. 2023 (2023), No. 23, pp. 1-11.

Title: Prescribed energy saddle-point solutions of nonlinear indefinite problems
       
Authors: Yavdat Il'yasov (Federal Research Centre, RAS, Ufa, Russia)
         Edcarlos D. Silva (Federal Univ. of Goias, GO, Brazil)
         Maxwell L. Silva (Federal Univ. of Goias, GO, Brazil)

Abstract:
A minimax variational method for finding mountain pass-type solutions with
prescribed energy levels is introduced. The method is based on application
of the Linking Theorem to the energy-level nonlinear Rayleigh quotients which
critical points correspond to the solutions of the equation with prescribed 
energy. An application of the method to nonlinear indefinite elliptic 
problems with nonlinearities that does not satisfy the 
Ambrosetti-Rabinowitz growth conditions is also presented.   

Submitted December 5, 2022. Published March 04, 2023
Math Subject Classifications: 35G15, 35G20, 35G25, 35G30.
Key Words: Indefinite problems; linking theorems; Rayleigh quotient.