Existence and uniqueness for a semilinear elliptic problem on Lipschitz domains in Riemannian manifolds II
Martin Dindoš · Transactions of the American Mathematical Society · 2002
Extending our recent work for the semilinear elliptic equation on Lipschitz domains, we study a general second-order Dirichlet problem L u − F ( x , u ) = 0 Lu-F(x,u)=0 in Ω \Omega . We improve our previous results by studying more general nonlinear terms F ( x , u ) F(x,u) with polynomial (and in some cases exponential) growth in the variable u u . We also study the case of nonnegative solutions.