A solution to a slightly subcritical elliptic problem with non-power nonlinearity

We consider a slightly subcritical Dirichlet problem with non-power nonlinearity in bounded smooth domain. For this problem, standard compact embeddings cannot be used to guarantee the existence of solutions as case power-type nonlinearities. Instead, we use Ljapunov-Schmidt reduction method show that there is positive solution which concentrates at non-degenerate critical point Robin function. This first result for type generalized problems.