Electronic Journal of Differential Equations,
Vol. 2011 (2011), No. 43, pp. 1-9.

Title: Existence and multiplicity of solutions for divergence type
       elliptic equations

Authors: Lin Zhao    (Lanzhou Univ., Gansu, China)
         Peihao Zhao (Lanzhou Univ., Gansu, China)
	 Xiaoxia Xie (Lanzhou Univ., Gansu, China)

Abstract:
 We establish the existence and multiplicity of weak solutions
 of a problem involving a uniformly convex elliptic operator
 in divergence form.
 We find one nontrivial solution by the mountain pass lemma,
 when the nonlinearity has a $(p-1)$-superlinear growth at infinity,
 and two nontrivial solutions by minimization and mountain pass
 when the nonlinear term has a $(p-1)$-sublinear growth at infinity.
 	 
Submitted January 1, 2011. Published March 31, 2011.
Math Subject Classifications: 35A15, 35J20, 35J62.
Key Words: Nonlinear elliptic equations; uniformly convex; 
           mountain pass lemma; three critical points theorem.