Zobrazeno 1 - 10
of 90
pro vyhledávání: '"Il'Yasov, Yavdat"'
Autor:
Il'yasov, Yavdat
We develop a novel method for finding bifurcations for nonlinear systems of equations based on directly finding bifurcations through saddle points of extended quotients. The method is applied to find the saddle-node bifurcation point for elliptic equ
Externí odkaz:
http://arxiv.org/abs/2405.02684
Autor:
Il'yasov, Yavdat
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 scaled extended quotient whose saddle points correspond to the saddle-node
Externí odkaz:
http://arxiv.org/abs/2404.05643
Autor:
Il'yasov, Yavdat, Valeev, Nurmukhamet
We develop the Perron-Frobenius theory using a variational approach and extend it to a set of arbitrary matrices, including those that are neither irreducible nor essentially positive, and non-preserved cones. We introduce a new concept called a quas
Externí odkaz:
http://arxiv.org/abs/2402.06458
Autor:
Il'yasov, Yavdat
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 is applied for solving an open problem on the existence of a maximal
Externí odkaz:
http://arxiv.org/abs/2303.10726
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 energy level nonlinear generalized Rayleigh quotients. An application to in
Externí odkaz:
http://arxiv.org/abs/2208.08928
We discuss the existence and non-existence of periodic in one variable and compactly supported in the other variables least energy solutions for equations with non-Lipschitz nonlinearity of the form: $-\Delta u=\lambda u^p - u^q$ in $\mathbb{R}^{N+1}
Externí odkaz:
http://arxiv.org/abs/2202.12522
We discuss the existence of multiple positive solutions leading to the occurrence of an S-shaped bifurcation curve to the equations of the form $$ -\Delta_p u= f(\mu,\lambda, u)~ \mbox{in} ~\Omega \subset \mathbb{R}^N $$ where $\Delta_p$ is a $p$-Lap
Externí odkaz:
http://arxiv.org/abs/2112.02329
Autor:
Il'yasov, Yavdat
The main topic of this note is a discussion of applicability conditions of the Nehari manifold method depending on the value of parameters of equations. As the main tool, we apply the nonlinear generalized Rayleigh quotient method.
Comment: 20 p
Comment: 20 p
Externí odkaz:
http://arxiv.org/abs/2108.00891
Autor:
Il'yasov, Yavdat
We prove orbital stability result for physical ground states of a nonlinear Schr\"{o}dinger (NLS) equation in the sense that the set of these ground states is contained in the set of prescribed mass solutions which is orbital stable by the Cazenave-L
Externí odkaz:
http://arxiv.org/abs/2103.16353
Autor:
Il'yasov, Yavdat
We introduce the nonlinear generalized Collatz-Wielandt formula $$ \lambda^*= \sup_{x\in Q}\min_{i:h_i(x) \neq 0} \frac{g_i(x)}{ h_i(x)}, ~~Q \subset \mathbb{R}^n,$$ and prove that its solution $(x^*,\lambda^*)$ yields the maximal saddle-node bifurca
Externí odkaz:
http://arxiv.org/abs/2003.12556