Geodesic
Existence and multiplicity of solutions for divergence type elliptic equations
Electronic Journal of Differential Equations, Tome 2011 (2011).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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.
Classification : 35A15, 35J20, 35J62
Keywords: nonlinear elliptic equations, uniformly convex, mountain pass lemma, three critical points theorem 
@article{EJDE_2011__2011__a54,
     author = {Zhao, Lin and Zhao, Peihao and Xie, Xiaoxia},
     title = {Existence and multiplicity of solutions for divergence type elliptic equations},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2011},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2011__2011__a54/}
}
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Zhao, Lin; Zhao, Peihao; Xie, Xiaoxia. Existence and multiplicity of solutions for divergence type elliptic equations. Electronic Journal of Differential Equations, Tome 2011 (2011). http://geodesic.mathdoc.fr/item/EJDE_2011__2011__a54/