Robin Boundary Value Problem for Some Nonlinear Nonlocal Elliptic Partial Differential Equations

This paper deals with Robin type boundary value problems for the mean field equation in the unit circle and for a nonlocal autonomous second order ordinary differential equation with cubic nonlinearity in the unit interval. The radial solutions in the first case and the classical solutions in the second one are written into explicit form. The real- valued spectral parameter can be bounded and unbounded and participates in the formulae for the corresponding solutions.