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In this paper, we consider a pseudo-parabolic system with nonlinearities of variable exponent type (ut - Δut - div(|∇u|m(x)-2∇u) = |uv|p(x)-2uv² in Ω x (0, T), (vt - Δvt - div(|∇v|n(x)-2∇v) = |uv|p(x)-2u²v in Ω x (0, T), associated with initial and Dirichlet boundary conditions, where the variable exponents p(·), m(·), n(·) are continuous functions on …. We obtain an upper bound and a lower bound for blow-up time if variable exponents p(·), m(·), n(·) and the initial data satisfy some conditions. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the position problem of limit cycles for a class of Liénard-type differential systems. By considering the upper bound of the amplitude of limit cycles on {(x, y) ∈ ℝ² : x < 0} and {(x, y) ∈ ℝ² : x > 0} respectively, we provide a criterion concerning an explicit upper bound for the amplitude of the unique limit cycle of the Liénard-type system on the plane. Here the amplitude of a limit cycle on {(x, y) ∈ ∈ : x < 0} (resp. {(x, y) ∈ ∈ : x > 0}) is defined as the minimum (resp. maximum) value of the x-coordinate on such a limit cycle. Finally, we give two examples including an application to predator-prey system model to illustrate the obtained theoretical result, and Matlab simulations are presented to show the agreement between our theoretical result with the simulation analysis. [ABSTRACT FROM AUTHOR]