An existence and nonexistence theorem for solutions of nonlinear systems and its application to algebraic equations

摘要

In this paper, we first present a componentwise existence and nonexistence theorem for solutions of nonlinear equations in Rn or Cn, which improves those of Alefeld (1986) and Yamamoto (1978,1979,1980,1984). Next, the theorem is applied to algebraic equations. Finally, the results are illustrated with examples.