Giovanni Molica Bisci and Dušan Repovš: Nonlinear Neumann problems driven by a nonhomogeneous differential operator, p.13-25


We study a nonlinear parametric Neumann problem driven by a nonhomogeneous quasilinear elliptic differential operator $\operatorname{div}(a(x,\nabla u))$, a special case of which is the $p$-Laplacian. The reaction term is a nonlinearity function $f$ which exhibits $(p-1)$-subcritical growth. By using variational methods, we prove a multiplicity result on the existence of weak solutions for such problems. An explicit example of an application is also presented.

Key Words: Three weak solutions, Variational methods, Divergence type equations.

2000 Mathematics Subject Classification: Primary: 35A15;
Secondary: 35J20, 35J62.

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