Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 39, 2014, 259-273

MULTIPLE SOLUTIONS FOR ELLIPTIC EQUATIONS INVOLVING A GENERAL OPERATOR IN DIVERGENCE FORM

Giovanni Molica Bisci and Dusan Repovs

University of Reggio Calabria, Department PAU
Via Melissari, 24 - 89124 Reggio Calabria, Italy; gmolica 'at' unirc.it

University of Ljubljana, Faculty of Education, and Faculty of Mathematics and Physics
POB 2964, Ljubljana, Slovenia 1001; dusan.repovs 'at' guest.arnes.si

Abstract. In this paper, exploiting variational methods, the existence of three weak solutions for a class of elliptic equations involving a general operator in divergence form and with Dirichlet boundary condition is investigated. Several special cases are analyzed. In conclusion, for completeness, a concrete example of an application is presented by finding the existence of three nontrivial weak solutions for an uniformly elliptic second-order problem on a bounded Euclidean domain.

2010 Mathematics Subject Classification: Primary 35J15, 35J25, 35J62, 35J92.

Key words: Three weak solutions, variational methods, divergence type equations.

Reference to this article: G. Molica Bisci and D. Repovs: Multiple solutions for elliptic equations involving a general operator in divergence form. Ann. Acad. Sci. Fenn. Math. 39 (2014), 259-273.

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doi:10.5186/aasfm.2014.3909