Electronic Journal of Differential Equations,
Vol. 2010(2010), No. 126, pp. 1-16.

Title: Positive solutions of boundary value problems with p-Laplacian

Authors: Qingkai Kong (Northern Illinois Univ., DeKalb, IL, USA)
         Min Wang (Northern Illinois Univ., DeKalb, IL, USA)

Abstract:
 In this article, we study a class of boundary value problems with
 p-Laplacian. By using a Green-like functional and applying the fixed
 point index theory, we obtain eigenvalue criteria for the existence of
 positive solutions. Several explicit conditions are derived as consequences,
 and further results are established for the multiplicity and nonexistence
 of positive solutions. Extensions are also given to partial differential
 BVPs with p-Laplacian defined on annular domains.

Submitted June 17, 2010. Published September 07, 2010.
Math Subject Classifications: 34B15, 34B18.
Key Words: Boundary value problem with p-Laplacian;
           positive solution;  existence and nonexistence; 
	   eigenvalue criteria; fixed point; index theory.