Abstract.
We study nonlinear nonlocal equations on a half-line in the critical case
where \(\beta \in {\mathbf{C}}\). The linear operator \({\mathbb{K}}\) is a pseudodifferential operator defined by the inverse Laplace transform with dissipative symbol \(K(p) = E_{\alpha}p^{\alpha}\), the number \(M = [\frac{\alpha} {2}]\). The aim of this paper is to prove the global existence of solutions to the inital-boundary value problem (0.1) and to find the main term of the large time asymptotic representation of solutions in the critical case.
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Kaikina, E.I., Guardado-Zavala, L., Ruiz-Paredes, H.F. et al. Critical Nonlinear Nonlocal Equations on a Half-Line. Nonlinear differ. equ. appl. 16, 63–77 (2009). https://doi.org/10.1007/s00030-008-0099-x
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DOI: https://doi.org/10.1007/s00030-008-0099-x