On Positive Solutions of Semilinear Elliptic Equations
Copyright policy )On Positive Solutions of Semilinear Elliptic Equations
This paper is concerned with necessary conditions for the existence of positive solutions of the semilinear problem Δ u + f ( u ) = 0 , x ∈ Ω , u = 0 , x ∈ ∂ Ω \Delta u + f(u) = 0,x \in \Omega ,u = 0,x \in \partial \Omega , whose supremum norm bears a certain relationship to zeros of the nonlinearity f f . We first discuss the smooth case (i.e., f f and ∂ Ω \partial \Omega smooth) and then show how to obtain similar results in the nonsmooth case.
positive solutions, semilinear, Boundary value problems for second-order elliptic equations, Nonlinear boundary value problems for linear elliptic equations, Smoothness and regularity of solutions to PDEs, existence, A priori estimates in context of PDEs, smooth
positive solutions, semilinear, Boundary value problems for second-order elliptic equations, Nonlinear boundary value problems for linear elliptic equations, Smoothness and regularity of solutions to PDEs, existence, A priori estimates in context of PDEs, smooth
citations This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).84 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Top 10% influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 1% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Top 10%
Citations provided by BIP!Popularity provided by BIP!