Solutions with sign information for nonlinear nonhomogeneous elliptic equations

Nikolaos S. Papageorgiou, Vicentiu D. Radulescu

DOI: http://dx.doi.org/10.12775/TMNA.2015.027

Abstract


We consider a class of nonlinear, coercive elliptic equations driven by a nonhomogeneous differential operator. Using variational methods together with truncation and comparison techniques, we show that the problem has at least three nontrivial solutions, all with sign information. In the special case of $(p,2)$-equations, using tools from Morse theory, we show the existence of four nontrivial solutions, all with sign information. Finally, for a special class of parametric equations, we obtain multiplicity theorems that substantially extend earlier results on the subject.

Keywords


Nonlinear nonhomogeneous differential operator; nonlinear maximum principle; strong comparison principle; Morse theory; parametric equations; nodal solutions

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