Prescribed energy saddle-point solutions of nonlinear indefinite problems
da Silva, Edcarlos Domingos
da Silva, Maxwell Lizete
Texas State University, Department of Mathematics
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.
Indefinite problems, Linking theorems, Rayleigh quotient
Il'yasov, Y., da Silva, E. D., & da Silva, M. L. (2023). Prescribed energy saddle-point solutions of nonlinear indefinite problems. <i>Electronic Journal of Differential Equations, 2023</i>(23), pp. 1-11.