Riv. Mat. Univ. Parma, Vol. 10, No. 1, 2019

Teresa Isernia[a]

On a nonhomogeneous sublinear-superlinear fractional equation in $$\mathbb{R}^{N}$$

Pages: 167-186
Accepted: 2 July 2019
Mathematics Subject Classification (2010): 35A15, 35J60, 35R11, 45G05.
Keywords: Fractional Laplacian, Sublinear growth, Nehari manifold, Concentration-compactness.
[a]: Dip. di Ingegneria Industriale e Scienze Matematiche, Università Politecnica delle Marche, Via Brecce Bianche 12, 60131 Ancona, Italy

Abstract: The existence of a positive solution to a nonhomogeneous fractional sublinear-superlinear problem in the whole space is proved by combining a minimization method, Nehari manifold and the fibering map methods, and the concentration-compactness lemma. We also study the continuity of solutions in the perturbation parameter $$f$$ at $$0$$.

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