Boundedness of Solutions for Semilinear Duffing Equations

Boundedness of solutions for semilinear duffing equations

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 Duffing’s Equations with Semilinear Potentials

Singular Solutions for some Semilinear Elliptic Equations

We are concerned with the behavior of u near x = O. There are two distinct cases: 1) When p >= N / ( N -2) and (N ~ 3) it has been shown by BR~ZIS & V~RON [9] that u must be smooth at 0 (See also BARAS & PIERRE [1] for a different proof). In other words, isolated singularities are removable. 2) When 1-< p < N / ( N 2) there are solutions of (1) with a singularity at x ---0. Moreover all singula...

Boundedness of Solutions to Linear Differential Equations

In the case of a linear constant coefficient differential equation, & = Ax, where x is a (complex) n-vector and A is a (complex) nXn matrix, it is well known when all solutions are bounded; namely, if all eigenvalues of A are purely imaginary and all elementary divisions of A are simple. This condition is equivalent to the Jordan normal form, / , of A being (Hermitian) skew symmetric. That is i...