Nonpositone elliptic problems in ${\bf R}\sp n$

W. Allegretto, P. O. Odiobala
1995 Proceedings of the American Mathematical Society  
We consider the problem of the existence of positive decaying solutions in R" to the nonlinear equation lu = Xf{x, u) where / denotes a second-order uniformly elliptic operator and f(x, u) is superlinear and subcritical with f(x, 0) < 0 . Existence is obtained by Mountain Pass Arguments and positivity by establishing bounds for u in various Sobolev norms and by comparison with the case / = -A .
doi:10.1090/s0002-9939-1995-1219715-9 fatcat:llmbwhkoebdtxh3jrrv236imvq