Boundedness for sublinear Duffing equations with time-dependent potentials

Boundedness for Semilinear Duffing Equations at Resonance

In this paper, we prove the boundedness of all solutions for the equation x + n 2 x + φ(x) + g (x)q(t) = 0, where n ∈ N, q(t) = q(t + 2π), φ(x) and g(x) are bounded.

Boundedness of solutions for semilinear duffing equations

Boundedness of Solutions for Duffing’s Equations with Semilinear Potentials

Differential Harnack Estimates for Time-dependent Heat Equations with Potentials

In this paper, we prove a differential Harnack inequality for positive solutions of time-dependent heat equations with potentials. We also prove a gradient estimate for the positive solution of the time-dependent heat equation.

Boundedness of solutions for sublinear reversible systems

In this paper we will study the boundedness of all solutions for second-order differential equations ẍ+ f(x)ẋ+ λx+ g(x) = p(t), where λ ∈ R and g(x) satisfies the sublinear growth condition. Since the system in general is non-Hamiltonian, we have to introduce reversibility assumptions to apply the twist theorem for reversible mappings. Under some suitable conditions we then obtain the existence...