Bifurcation analysis for a singular differential system with two parameters via to topological degree theory

Abstract

Based on the relation between Leray-Schauder degree and a pair of strict lower and upper solutions, we focus on the bifurcation analysis for a singular differential system with two parameters, explicit bifurcation points for relative parameters are obtained by using the property of solution for the akin systems and topological degree theory.

Multiple solutions for a modified quasilinear Schrödinger elliptic equation with a nonsquare diffusion term

“…Many mathematical methods, such as dual approach [3,22,[24][25][26], iterative techniques [19,[27][28][29][30], fixed point theorem [5,14,21], variational methods [6,15,23] and normal boundary intersection method [9,10], have been employed to solve the properties and control problems for various differential equations. In particular, by using a constrained minimization argument Poppenberg et al [15] established the existence of positive ground state solution for quasilinear Schrödinger equation (4).…”

Improving dynamics of integer-order small-world network models under fractional-order PD control

“…A Hopf bifurcation is a strategy for handling various dynamic properties of nonlinear systems, ranging from the equilibrium point, periodic oscillation, and chaos [17][18][19][20]. More detailed information about the performance of periodic solutions around the equilibrium can be derived following specific Hopf bifurcation analysis.…”

Extragradient subgradient methods for solving bilevel equilibrium problems

“…In 2008, Tran et al [25] proposed the extragradient algorithm for solving the equilibrium problem by using the strongly convex minimization problem to solve at each iteration. Furthermore, Hieu [9] introduced subgradient extragradient methods for pseudomonotone equilibrium problem and the other methods (see the details in [1, 8, 10, 15, 17, 22, 28]).…”