On the Convergence of a Class of Nonlocal Elliptic Equations and Related Optimal Design Problems
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DOI: 10.1007/s10957-016-1021-z
Abstract: A convergence result for a nonlocal differential equation problem is proved. As a by-product, some results about the convergence for a type of nonlocal optimal design are given. Since these problems give rise to local… read more here.
Keywords: design; convergence class; nonlocal elliptic; class nonlocal ... See more keywords
Nonlocal Elliptic Systems Involving Critical Sobolev-Hardy Exponents and Concave-convex Nonlinearities
Sign Up to like & getrecommendations! Published in 2019 at "Taiwanese Journal of Mathematics"
DOI: 10.11650/tjm/190109
Abstract: In this paper, a system of fractional elliptic equation is investigated, which involving fractional critical Sobolev-Hardy exponent and concave-convex terms. By means of variational methods and analytic techniques, the existence and multiplicity of positive solutions… read more here.
Keywords: concave convex; elliptic systems; sobolev hardy; critical sobolev ... See more keywords
Multiple Solutions for Nonlocal Elliptic Systems Involving p(x)-Biharmonic Operator
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DOI: 10.3390/math7080756
Abstract: This paper analyzes the nonlocal elliptic system involving the p(x)-biharmonic operator. We give the corresponding variational structure of the problem, and then by means of Ricceri’s Variational theorem and the definition of general Lebesgue-Sobolev space,… read more here.
Keywords: multiple solutions; involving biharmonic; solutions nonlocal; nonlocal elliptic ... See more keywords
On some local-nonlocal elliptic equation involving nonlinear terms with exponential growth
Sign Up to like & getrecommendations! Published in 2017 at "Communications on Pure and Applied Analysis"
DOI: 10.3934/cpaa.2017086
Abstract: In this paper, we prove the existence of multiple solutions to some intermediate local-nonlocal elliptic equation in the whole two dimensional space. The nonlinearities exhibit an exponential growth at infinity. read more here.
Keywords: elliptic equation; nonlocal elliptic; local nonlocal; exponential growth ... See more keywords