5 papers
Existence and uniqueness of a saddle-node bifurcation point for nonlinear equations in general domains
Yavdat Il'yasov
This paper provides a direct method of establishing the existence and uniqueness of saddle-node bifurcations for nonlinear equations in general domains. The method employs the scal…
A finding of the maximal saddle-node bifurcation for systems of differential equations
Yavdat Il'yasov
A variational method is presented for directly finding the bifurcation point of nonlinear equations as the saddle-node point of the extended nonlinear Rayleigh quotient. The method…
On prescribed energy saddle-point solutions to indefinite problems
Yavdat Il'yasov, Edcarlos D. Silva, Maxwell L. Silva
A minimax variational principle for saddle-point solutions with prescribed energy levels is introduced. The approach is based on the development of the linking theorem to the energ…
Existence of S-shaped type bifurcation curve with dual cusp catastrophe via variational methods
Marcos Leandro Carvalho, Yavdat Il'yasov, Carlos Alberto Santos
We discuss the existence of multiple positive solutions leading to the occurrence of an S-shaped bifurcation curve to the equations of the form $$ -Δ_p u= f(μ,λ, u)~ \mbox{in} ~Ω\s…
Flat solutions of some non-Lipschitz autonomous semilinear equations may be stable for
Jesús Ildefonso Díaz, Jesús Hernández, Yavdat Il'yasov
We prove that flat ground state solutions ( minimizing the energy and with gradient vanishing on the boundary of the domain) of the Dirichlet problem associated to some semil…