Abstract
In this paper, we prove the existence of a solution between a well-ordered subsolution and supersolution of a class of nonlocal elliptic problems and give some degree information. Using the method and bifurcation theory, we present the existence and multiplicity of positive solutions for the nonlocal problems with the changes of the parameter.
Highlights
In this paper, we consider the following problem:⎧ ⎪⎨ –a( |u|γ dx) u = fλ(x, u), x in, ⎪⎩ u u > =, x in, x on ∂, ( . )where ⊆ RN is a smooth bounded domain, γ ∈ (, +∞), and a : [, +∞) → (, +∞) is a continuous function with inf a(t) ≥ a = a( ) > . t∈[,+∞)Chipot and Lovat [ ] considered the following model problem:⎧ ⎪⎨ ut – a( u(z, t) dz) u = f in u(x, u(x, t) = ) = u on (x)
[ ] established the sub-supersolution method, which can be used to study the existence of weak solutions for a large class of nonlocal problems
Motivated by the works of [, ], in this paper, we study the existence and multiplicity of the classical positive solutions for ( . )
Summary
Variational methods are used to consider the existence of the solutions to [ ] established the sub-supersolution method, which can be used to study the existence of weak solutions for a large class of nonlocal problems. Section presents the existence and multiplicity of positive solutions to
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