The Hyers-Ulam stability of a functional equation deriving from quadratic and cubic functions in quasi-β-normed spaces

On the Reducibility of Quasiperiodic Linear Hamiltonian Systems and Its Applications in Schrödinger Equation

“…One can see Section 4 for more details about this example. There are plenty of works about the stability of all kinds of equations, one can refer to [16][17][18][19][20][21][22][23] for a detailed description. In particular, for quasiperiodic equations, in order to determine the type of stability of the equilibria of quasiperiodic Hamiltonian systems, the authors need to assume that the corresponding linearized system is reducible, and some conditions were added to the system after the reducibility.…”

Existence of Nontrivial Solutions for Fractional Differential Equations with p-Laplacian

“…With the rapid development of the theory of fractional differential equations, during the last two decades, the existence of nontrivial solutions of fractional differential equations has been studied by many researchers in nonsingular case as well as singular case. See [6][7][8][9][10][11][12][13][14][15][16][17][18][19]. Usually, the proof is based on either the method of upper and lower solutions, fixed point theorems, alternative principle of Leray-Schauder, topological degree theory, or critical point theory.…”

Mean-Square Exponential Input-to-State Stability of Stochastic Fuzzy Recurrent Neural Networks with Multiproportional Delays and Distributed Delays

“…On one hand, the switching speed of amplifier is limited and the errors occur in electronic components. As a consequence, delays happen to dynamics systems, and the delays often destroy the stability of dynamics systems, even cause the heavy oscillation (e.g., see [25][26][27][28][29][30][31][32][33][34][35]). So it is significant to study the stability of delayed neural networks.…”