Semilinear Duffing Equations Crossing Resonance Points

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

Semilinear Elliptic Equations and Fixed Points

In this paper, we deal with a class of semilinear elliptic equation in a bounded domain Ω ⊂ R , N ≥ 3, with C boundary. Using a new fixed point result of the Krasnoselskii’s type for the sum of two operators, an existence principle of strong solutions is proved. We give two examples where the nonlinearity can be critical.

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

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.