Positive solutions for a class of equations with a \(p\)-Laplace like operator and weights
The paper deals with the existence of positive solutions for the problem \[ (a(r)\varphi(u'))'+b(r)g(u)=0 \quad \text{ a.e. in}\;(0,R), \] \[ \lim_{r\to 0}a(r)\varphi(u'(r))=0, \quad u(R)=0, \] where \(\varphi\) is an odd increasing homeomorphism of \(\mathbb R\) and \(a\) and \(b\) are weight functions. To prove the main result of the paper the authors apply the Leray-Schauder degree technique. In particular, a new identity of Pohozaev type is established and used to obtain a priori bounds for positive solutions.
scientific article; zbMATH DE number 5569423