Positive Solution for the Elliptic Problems with Sublinear and Superlinear Nonlinearities. (22nd December 2010)

• Record Type: Journal Article
• Authors: Yuan, Chunmei; Guo, Shujuan; Tong, Kaiyu
• Other Names: Chou Jyh Horng Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2010(2010)
• Publication Date: 2010-12-22
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2010/640841
• Languages: English
• ISSNs: 1024-123X

Abstract

Abstract : This paper deals with the existence of positive solutions for the elliptic problems with sublinear and superlinear nonlinearities- Δ u = λ a ( x ) u p + b ( x ) u q inΩ, u > 0 inΩ, u = 0 on∂ Ω, whereλ > 0 is a real parameter, 0 < p < 1 < q .Ω is a bounded domain inℝ N ( N ≥ 3 ), anda ( x ) andb ( x ) are some given functions. By means of variational method and super-subsolution method, we obtain some results about existence of positive solutions.