Banach空间中带紧扰动或具紧预解式的增生算子的满射定理

Surjectirity Theorems Involving Compact Perturbations and Compact Resolvents of Accretive Operators in Banach Spaces

本文的目的是研究算子方程Tx+Cx=f的可解性问题,其中T为增生算子,C为紧的或连续有界算子。用度理论,主要是Leray-Schauder度理论建立了一些满射定理,这些结果是作者[12]的继续,且推广和改进了Kartsatos[7,9]及Hirano[5]中的有关结果。

In this paper we study the solvability of the equation Tx+Cx = f where T is an accretive operator and C is compact or both continuous and bounded opera-tor.The methods employed in this paper involve degree theory argument. We establish some surjectivity theorems by using the theorey of Leray-schauder degree and solving the approximating equations Tx+Cx+( 1 / n)x = f. Our theorems complement and extend certain results of the author in[12],of Kartsatos in [7,9]and of Hirano[5].