Electronic Journal of Differential Equations, Vol. 2025 (2025), No. 66, pp. 1-15.

Title: Solutions to nonlinear elliptic problems with nonhomogeneous operators and mixed nonlocal boundary conditions

Authors: Eun Kyoung Lee (Pusan National Univ, Busan, Korea)
         Inbo Sim (Univ. of Ulsan, Korea)
         Byungjae Son (Ohio Northern Univ., OH, USA)

Abstract:
We investigate the existence, multiplicity and nonexistence of positive solutions to
nonlinear (singular) elliptic problems involving nonhomogeneous operators and mixed
nonlocal boundary conditions based on the behaviors of the nonlinear term near $0$
and $\infty$. In particular, we discuss the existence of at least three positive
solutions to the mixed nonlocal boundary problems, which is new finding even for
the problems involving homogeneous operators. The novelty of this study lies in
constructing completely continuous operators related to nonlinear elliptic problems
involving complicated boundary conditions. We emphasize that only one fixed point
theorem is used to obtain the existence and multiplicity results, despite generalizing
and extending most of the problems in previous literature.


Submitted February 20, 2025. Published June 30, 2025.
Math Subject Classifications: 34B10, 34B16, 34B18.
Key Words: Singular elliptic problem; nonhomogeneous operator; integral boundary condition;  multipoint boundary condition; positive solution.