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In this article, we consider the existence of ground state positive solutions for nonlinear Schrodinger equations of the fractional (p, q)-Laplacian with Rabinowitz potentials defined in R-n,

(-Delta)(p)(s1) u + (-Delta)(q)(s2) q u+ V(epsilon x)(vertical bar u vertical bar(p-2)u+vertical bar u vertical bar(q-2)u) =lambda f(u) + sigma vertical bar u vertical bar q*(-2)(s2)u.

We prove existence by confining different ranges of the parameter lambda under the subcritical or critical nonlinearities caused by sigma = 0 or 1, respectively. In particular, a delicate calculation for the critical growth is provided so as to avoid the failure of a global Palais-Smale condition for the energy functional.


© 2021.

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Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.

Publication Title

Electron. J. Differential Equations

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Mathematics Commons



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