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
A nonlocal elliptic system with nonlinear singular terms
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DOI: 10.1080/17476933.2024.2382791
Abstract: In this work we deal with the nonlocal elliptic system: \[ \it{(S)} \begin{cases} (-\Delta)^{s_1} u = \theta\frac{v^q}{u^{1-\theta}} & {\rm in}\ \Omega , \\ (-\Delta)^{s_2} v = qv^{q-1}u^\theta & {\rm in}\ \Omega , \\ u =v… read more here.
Keywords: system; singular terms; nonlocal elliptic; system nonlinear ... See more keywords
Nonlocal Elliptic Systems Involving Critical Sobolev-Hardy Exponents and Concave-convex Nonlinearities
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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
Exact solutions and bifurcation curves of nonlocal elliptic equations with convolutional Kirchhoff functions
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DOI: 10.1186/s13661-024-01871-1
Abstract: We study the one-dimensional nonlocal elliptic equation of Kirchhoff type with convolutional Kirchhoff functions. We establish the exact solutions u λ $u_{\lambda}$ and bifurcation curves λ ( α ) $\lambda (\alpha )$ , where α… read more here.
Keywords: exact solutions; bifurcation curves; nonlocal elliptic; kirchhoff functions ... See more keywords
Regularizing Effects for Some Nonlocal Elliptic Problems
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DOI: 10.3390/math13050687
Abstract: We study the regularizing effect of the zero order term in some elliptic problems, which present in the principal part a nonlocal operator, i.e., the fractional Laplacian operator. We prove the existence of bounded energy… read more here.
Keywords: elliptic problems; nonlocal elliptic; effects nonlocal; regularizing effects ... 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
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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