Existence results for nonlinear elliptic equations in bounded domains of ℝn
Texas State University-San Marcos, Department of Mathematics
We establish existence results for the boundary-value problem Δu + ƒ(., u) = 0 in a smooth bounded domain in ℝn (n ≥ 2), where ƒ satisfies some appropriate conditions related to a Kato class. The proofs are based on various techniques related to potential theory.
Green function, Elliptic equation, Positive solutions
Zribi, M. (2006). Existence results for nonlinear elliptic equations in bounded domains of ℝn. <i>Electronic Journal of Differential Equations, 2006</i>(92), pp. 1-11.