Strongly nonlinear elliptic problem without growth condition.(English)Zbl 1109.35331

Summary: We study a boundary-value problem for the $$p$$-Laplacian with a nonlinear term. We assume only coercivity conditions on the potential and do not assume growth condition on the nonlinearity. The coercivity is obtained by using similar nonresonance conditions.

MSC:

 35J60 Nonlinear elliptic equations 35J20 Variational methods for second-order elliptic equations 35J25 Boundary value problems for second-order elliptic equations 47J30 Variational methods involving nonlinear operators

Keywords:

$$p$$-Laplacian; growth condition
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