Semilinear p-evolution equations in Sobolev spaces

Abstract

We prove local in time well-posedness in Sobolev spaces of the Cauchy problem for semi-linear p-evolution equations of the first order with real principal part, but complex valued coefficients for the lower order terms, assuming decay conditions on the imaginary parts as |x| goes to infinity.

References in corpus (1)

• A necessary condition for $H^{\infty }$ well-posedness of p-evolution equations

Cited by in corpus (3)

• Gevrey well posedness for $3$-evolution equations with variable coefficients
• A necessary condition for $H^{\infty }$ well-posedness of p-evolution equations
• Schrödinger-type equations in Gelfand-Shilov spaces