Abstract: Consider the equation −ε 2 Δu ε + q(x)u ε = f(u ε ) in , ∣u(∞)∣<∞, ε =const>0. Under what assumptions on q(x) and f(u) can one prove that the solution u ε exists and lim ε→0 u ε = u(x), where u(x) solves the limiting problem q(x)u = f(u)? These are the questions discussed in the paper. [Copyright &y& Elsevier]
In this paper, we consider a fractional Schrödinger equation with steep potential well and sublinear perturbation. By virtue of variational methods, the existence criteria of infinitely many nontrivial high or small energy solutions are established. In addition, the phenomenon of the concentration of solutions is also explored. We also give some examples to demonstrate the main results. [ABSTRACT FROM AUTHOR]