A variational inequality index for condensing maps in Hilbert spaces and applications to semilinear elliptic inequalities

作者：Lan, K Q^*; Lin, W

来源：Nonlinear Analysis-Theory Methods & Applications, 2011, 74(16): 5415-5425.

DOI：10.1016/j.na.2011.05.025

• Variational inequality index
• Condensing maps
• Semilinear elliptic inequalities

A variational inequality index for gamma-condensing maps is established in Hilbert spaces. New results on existence of nonzero positive solutions of variational inequalities for such maps are proved by using the theory of variational inequality index. Applications of such a theory are given to existence of nonzero positive weak solutions for semilinear second order elliptic inequalities, where previous results of variational inequalities for S-contractive maps cannot be applied.

• 出版日期2011-11
• 单位复旦大学