On Some $\protect \overrightarrow {p(x)}$ Anisotropic Elliptic Equations in Unbounded Domain
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DOI: 10.1007/s40306-021-00434-1
Abstract: We study a class of nonlinear elliptic problems with Dirichlet conditions in the framework of the Sobolev anisotropic spaces with variable exponent, involving an anisotropic operator on an unbounded domain ${\varOmega }\subset \mathbb {R}^{N} (N… read more here.
Keywords: unbounded domain; protect overrightarrow; anisotropic; overrightarrow anisotropic ... See more keywords
Existence of solutions for a fractional equation in an unbounded domain
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DOI: 10.1063/1.5121762
Abstract: This paper focuses on the scalar field equation Dx2αu−νu−uyy=f(u), where α ∈ (0, 1), (x,y)∈RN×(−L,L)⊂RN+1, with N ≥ 1 and Dx2α stands for the fractional Laplacian. By using several variational methods, we establish the existence,… read more here.
Keywords: unbounded domain; solutions fractional; existence solutions; fractional equation ... See more keywords
The entropy solution of a reaction–diffusion equation on an unbounded domain
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DOI: 10.1186/s13660-019-1956-3
Abstract: The degenerate parabolic equations from the reaction–diffusion problems are considered on an unbounded domain Ω⊂RN$\varOmega\subset\mathbb {R}^{N}$. It is expected that only a partial boundary should be imposed the homogeneous boundary value, but how to give… read more here.
Keywords: partial boundary; reaction diffusion; unbounded domain;
Regularized Solution of the Cauchy Problem in an Unbounded Domain
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DOI: 10.3390/sym14081682
Abstract: In this paper, using the construction of the Carleman matrix, we explicitly find a regularized solution of the Cauchy problem for matrix factorizations of the Helmholtz equation in a three-dimensional unbounded domain. read more here.
Keywords: solution cauchy; unbounded domain; cauchy problem; regularized solution ... See more keywords