Perturbations of Lane-Emden and Hamilton-Jacobi equations: The full space case

作者：Ai Shangbing; Cowan Craig^*

来源：Nonlinear Analysis-Theory Methods & Applications, 2017, 151: 227-251.

DOI：10.1016/j.na.2016.12.005

• Lane-Emden
• Viscous Hamilton-Jacobi
• Fullspace

In this article we are interested in positive classical solutions of
-Delta u +a(x) . Vu + V(x)u = u(p) + gamma u(q) in R-N,
and
du + -Delta u+ a(x) . Vu = u(P) + gamma vertical bar del u vertical bar(q) in R-N,
in the case of N >= 4, p > N+1/N-3 and gamma is an element of R. We assume that V is a smooth nonnegative potential and a(x) is a smooth vector field, both of which satisfy natural decay assumptions. Under suitable assumptions on q we prove the existence of positive classical solutions.

• 出版日期2017-3