Solutions of nonlinear hyperbolic equations at resonance

Solutions of Nonlinear Hyperbolic Equations at Resonance

Existence of solutions of nonlinear fractional differential equations at resonance

In this paper we study the existence of solutions of nonlinear fractional differential equations at resonance. By using the coincidence degree theory due to Mawhin, the existence of solutions is obtained.

On Finite Closures of Homogenized Solutions of Nonlinear Hyperbolic Equations

We study nonlinear equations subject to oscillatory initial data. The oscillatory solution of such problems tends to a homogenized weak limit that is characterized by the corresponding homogenized equations. Those equations usually involve an additional independent variable, so that the weak limit is an average of infinitely many functions. In certain cases, however, there is an alternative des...

Numerical Verifications of Solutions for Nonlinear Hyperbolic Equations

In this paper, we consider a numerical technique to enclose the solutions with guaranteed error bounds for nonlinear hyperbolic initial boundary value problems as well as to verify the existence of solutions. Using a finite element approximation and explicit error estimates for a certain simple linear hyperbolic problem, we construct, by computer, a set of functions which satisfies the conditio...

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