Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 139, pp. 1-9.

Title: Semilinear elliptic equations with dependence on the gradient

Authors: Guanggang Liu (Jilin Univ., Changchun, China)
         Shaoyun Shi   (Jilin Univ., Changchun, China)
	 Yucheng Wei   (Jilin Univ., Changchun, China)

Abstract:
 In this article we consider elliptic equations whose nonlinear term
 depends on the gradient of the unknown. We assume that the nonlinearity  
 has a asymptotically linear growth at zero and at infinity
 with respect to the second variable. By applying Morse theory  and
 an iterative method, we prove the existence of nontrivial solutions.
 
Submitted April 17, 2012. Published August 19, 2012.
Math Subject Classifications: 35J20, 35J25, 35J60.
Key Words: Semilinear equation; Morse theory; critical group; iterative method.