We study the large-time behavior of solutions for the inhomogeneous nonlinear Schrödinger equation iut+Δu=λ|u|p+μ|∇u|q+w(x),t>0,x∈RN,where N≥ 1 , p, q> 1 , λ, μ∈ C, λ≠ 0 , and u(0,·),w∈Lloc1(RN,C). We consider both the cases where μ= 0 and μ≠ 0 , respectively. We establish existence/nonexistence of global weak solutions. In each studied case, we compute the critical exponents in the sense of Fujita, and Lee and Ni. When μ≠ 0 , we show that the nonlinearity | ∇ u| q induces an interesting phenomenon of discontinuity of the Fujita critical exponent.

Alotaibi M., Jleli M., Samet B., Vetro C. (2022). First and second critical exponents for an inhomogeneous Schrödinger equation with combined nonlinearities. ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 73, 1-17 [10.1007/s00033-022-01784-y].

First and second critical exponents for an inhomogeneous Schrödinger equation with combined nonlinearities

Vetro C.
2022

Abstract

We study the large-time behavior of solutions for the inhomogeneous nonlinear Schrödinger equation iut+Δu=λ|u|p+μ|∇u|q+w(x),t>0,x∈RN,where N≥ 1 , p, q> 1 , λ, μ∈ C, λ≠ 0 , and u(0,·),w∈Lloc1(RN,C). We consider both the cases where μ= 0 and μ≠ 0 , respectively. We establish existence/nonexistence of global weak solutions. In each studied case, we compute the critical exponents in the sense of Fujita, and Lee and Ni. When μ≠ 0 , we show that the nonlinearity | ∇ u| q induces an interesting phenomenon of discontinuity of the Fujita critical exponent.
Settore MAT/05 - Analisi Matematica
https://link.springer.com/article/10.1007/s00033-022-01784-y
Alotaibi M., Jleli M., Samet B., Vetro C. (2022). First and second critical exponents for an inhomogeneous Schrödinger equation with combined nonlinearities. ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 73, 1-17 [10.1007/s00033-022-01784-y].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/569026
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