Positive solutions for a two point nonlinear boundary value problem with applications to semilinear elliptic equations. (English) Zbl 0879.34027

The authors consider an elliptic problem on the punctured ball including, for example, the one for the elliptic equation with the well-known Emden-Fowler nonlinearity as a special case. This existence problem turns out to be transformable to the Dirichlet (possibly singular) boundary value problem for a second-order ordinary differential equation without friction. Using the mountain pass lemma, sharp existence criteria are obtained for positive solutions of the Dirichlet problem, and subsequently for radial solutions of the elliptic problem. Examples illustrate the wide class of equations to which the results apply.
Reviewer: J.Andres (Olomouc)


34B15 Nonlinear boundary value problems for ordinary differential equations
35J25 Boundary value problems for second-order elliptic equations