A new method for the boundedness of semilinear Duffing equations at resonance

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

Unbounded solutions of semilinear equations at resonance

We consider a forced harmonic oscillator at resonance with a nonlinear perturbation and obtain a sharp condition for the existence of unbounded motions. Such a condition is extended to the case of a semilinear vibrating string. AMS classification scheme numbers: 34C11, 35L05

Boundedness of Solutions for Duffing’s Equations with Semilinear Potentials

Nontrivial solutions of elliptic semilinear equations at resonance

We find nontrivial solutions for semilinear boundary value problems having resonance both at zero and at infinity.