Nonlinear Elliptic Equations in R without Growth Restrictions on the Data
نویسندگان
چکیده
We show existence and regularity of solutions in R to nonlinear elliptic equations of the form −div A(x, Du) + g(x, u) = f , when f is just a locally integrable function, under appropriate growth conditions on A and g but not on f . Roughly speaking, in the model case −∆p(u) + |u|s−1u = f , with p > 2 − (1/N), existence of a nonnegative solution in R is guaranteed for every nonnegative f ∈ Lloc(R ) if and only if s > p− 1. AMS Classification: 35J60, 35J70.
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