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http://dx.doi.org/10.4134/JKMS.j170681

INFINITELY MANY SMALL ENERGY SOLUTIONS FOR EQUATIONS INVOLVING THE FRACTIONAL LAPLACIAN IN ℝN  

Kim, Yun-Ho (Department of Mathematics Education Sangmyung University)
Publication Information
Journal of the Korean Mathematical Society / v.55, no.5, 2018 , pp. 1269-1283 More about this Journal
Abstract
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.
Keywords
integrodifferential operators; fractional Laplacian; variational methods; infinitely many solutions;
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