On a radial positive solution to a nonlogical elliptic equation. (English) Zbl 1112.35068

Fijałkowski, Piotr; Przeradzki, Bogdan

Topol. Methods Nonlinear Anal. 21, No. 2, 293-300 (2003).

The paper deals with Dirichlet boundary value problem for the nonlinear Poisson equation with nonlocal term \[ - \Delta u = f (u, \int_U g \circ u) \]
\[ u| _{\partial U} = 0, \] where \(U\) is assumed to be an annulus or a ball. Existence of solutions is obtained via fixed point theorems for increasing compact operators.

Reviewer: Emil Minchev (Russe)

MSC:

35J60	Nonlinear elliptic equations
35J25	Boundary value problems for second-order elliptic equations
47H10	Fixed-point theorems
47N20	Applications of operator theory to differential and integral equations

Keywords:

nonlocal elliptic equation; radial solution; fixed point