Abstract
We consider the fractional advection dispersion equation in $\mathbb {R}^{N}$ . The nonlinearity is superlinear but does not satisfy the Ambrosetti-Rabinowitz type condition. We obtain the existence of nontrivial solutions of the equations, improving a recent result of Zhang-Sun-Li (Appl. Math. Model. 38:4062-4075, 2014).
Highlights
1 Introduction and main results In this paper we are concerned with the following fractional advection dispersion equation:
We look for solution of (P) in the space
2 Preliminaries we introduce some basic definitions and properties of the fractional calculus which are used further in this paper
Summary
There exist r > and ρ > , such that φ(u) ≥ ρ > , u = r. Equation ( ) implies that φc separates γ ( ) = and γ ( ) = η , and there exists a (C)c sequence {un} for φ. If {un} is unbounded, up to a subsequence we may assume that φ(un) → c, un → +∞, φ (un) un →. It is easy to see that the number of points in ZN ∩ B (yn) is less than N ; there exists zn ∈ B (yn) such that. Passing to a subsequence we have wn → w in L loc RN and wn(x) → w(x) a.e. x ∈ RN
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