The Nonzero Solutions and Multiple Solutions for a Class of Bilinear Variational Inequalities
© Jianhua Huang 2007
Received: 24 May 2007
Accepted: 29 June 2007
Published: 19 August 2007
Some existence theorems of nonzero solutions and multiple solutions for a class of bilinear variational inequalities are studied in reflexive Banach spaces by fixed point index approach. The results presented in this paper improve and extend some known results in the literature.
- Chang SS: Variational Inequality and Complementarity Problem Theory with Applications. Shanghai Scientific Technology and Literature Press, Shanghai, China; 1991.Google Scholar
- Noor MA: On a class of variational inequalities. Journal of Mathematical Analysis and Applications 1987,128(1):138–155. 10.1016/0022-247X(87)90221-6MathSciNetView ArticleMATHGoogle Scholar
- Zhang SS, Xiang SW: On the existence and uniqueness of solutions for a class of variational inequalities with applications to the Signorini problem in mechanics. Applied Mathematics and Mechanics 1991,12(5):401–407.MathSciNetGoogle Scholar
- Wu K-Q, Huang N-J: Non-zero solutions for a class of generalized variational inequalities in reflexive Banach spaces. Applied Mathematics Letters 2007,20(2):148–153. 10.1016/j.aml.2006.03.009MathSciNetView ArticleMATHGoogle Scholar
- Guo DJ: Nonlinear Functional Analysis. Science and Technology Press, Jinan, Shandong, China; 1985.Google Scholar
- Lloyd NG: Degree Theory. Cambridge University Press, Cambridge, UK; 1975.Google Scholar
- Showalter RE: Monotone Operators in Banach Space and Nonlinear Partial Differential Equations, Mathematical Surveys and Monographs. Volume 49. American Mathematical Society, Providence, RI, USA; 1997:xiv+278.Google Scholar
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