Abstract: Under weak conditions on the diffusion coefficients, we prove existence theorems of weak solutions for some nonlinear nonlocal elliptic problems. Our approach is based on the Schauder fixed point theorem combined with an approximation technique. We also give uniqueness results and an example to support them.
Keywords: nonlinear nonlocal elliptic problem; diffusion coefficient; fixed point; weak solution; existence; uniqueness
DOI: DOI 10.14712/1213-7243.2025.011
AMS Subject Classification: 35D30 35J60