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We are concerned with elliptic equations in $\mathbb R^N$, driven by a non-local integro-differential operator, which involves the fractional Laplacian. The main aim of this paper is to prove the existence of small solutions for our problem with negative energy in the sense that the sequence of solutions converges to $0$ in the $L^{\infty}$-norm by employing the regularity type result on the $L^{\infty}$-boundedness of solutions and the modified functional method.
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참고문헌 (36)
참고문헌 신청
R. A. Adams / 2003 / Sobolev Spaces / Elsevier/Academic Press
A. Ambrosetti / 1973 / Dual variational methods in critical point theory and applications / J. Functional Analysis 14:349~381
G. Autuori / 2013 / Elliptic problems involving the fractional Laplacian in ${\mathbb{R}}^N$ / J. Differential Equations 255(8):2340~2362
B. Barrios / 2012 / On some critical problems for the fractional Laplacian operator / J. Differential Equations 252(11):6133~6162
J. Bertoin / 1996 / Levy Processes, Cambridge Tracts in Mathematics, 121 / Cambridge University Press
A. Ambrosetti / 1973 / Dual variational methods in critical point theory and applications / J. Functional Analysis 14:349~381
G. Autuori / 2013 / Elliptic problems involving the fractional Laplacian in
B. Barrios / 2012 / On some critical problems for the fractional Laplacian operator / J. Differential Equations 252(11):6133~6162
J. Bertoin / 1996 / Levy Processes, Cambridge Tracts in Mathematics, 121 / Cambridge University Press
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