On a class of problems involving a nonlocal operator. (English) Zbl 1086.35038
Summary: We prove a result on existence of positive solution for a nonlocal elliptic problem by using a result on Fixed Point Index Theory and we establish another existence result which is proved by sub and supersolution and a Comparison Principle. Moreover, we prove the existence, uniqueness and asymptotic behaviour of the solutions for the evolution case.
MSC:
| 35J60 | Nonlinear elliptic equations |
| 35J20 | Variational methods for second-order elliptic equations |
| 35J25 | Boundary value problems for second-order elliptic equations |
| 47J05 | Equations involving nonlinear operators (general) |
Keywords:
Nonlocal elliptic equation; Asymptotic behaviour of the solutions; Existence and uniqueness for the evolution case; Positive solutions and comparison principleReferences:
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