We consider the semi-linear fractional Schrödinger equation
{(−Δ)su+V(x)u=f(x,u),x∈RN,u∈Hs(RN),
where both V(x) and f(x,u) are periodic in x, 0 belongs to a spectral gap of the operator (−Δ)s+V and f(x,u) is subcritical in u. We obtain the existence of nontrivial solutions by using a generalized linking theorem, and based on this existence we further establish infinitely many geometrically distinct solutions. We weaken the super-quadratic condition of f, which is usually assumed even in the standard Laplacian case so as to obtain the existence of solutions.
Citation: Jian Wang, Zhuoran Du. Multiple entire solutions of fractional Laplacian Schrödinger equations[J]. AIMS Mathematics, 2021, 6(8): 8509-8524. doi: 10.3934/math.2021494
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We consider the semi-linear fractional Schrödinger equation
{(−Δ)su+V(x)u=f(x,u),x∈RN,u∈Hs(RN),
where both V(x) and f(x,u) are periodic in x, 0 belongs to a spectral gap of the operator (−Δ)s+V and f(x,u) is subcritical in u. We obtain the existence of nontrivial solutions by using a generalized linking theorem, and based on this existence we further establish infinitely many geometrically distinct solutions. We weaken the super-quadratic condition of f, which is usually assumed even in the standard Laplacian case so as to obtain the existence of solutions.
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Jian Wang, Zhuoran Du. Multiple entire solutions of fractional Laplacian Schrödinger equations[J]. AIMS Mathematics, 2021, 6(8): 8509-8524. doi: 10.3934/math.2021494
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