Existence of entire solutions for a class of variable exponent elliptic equations

By Patrizia Pucci, Qihu Zhang. 2014

109 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/331e5a1f1685243c3e3bef30e260354540c08a03

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

Existence of Positive Solutions for p(x)-Laplacian Equations with a Singular Nonlinear Term (2014, background): “For example, the regularity of weak solutions for differential equations with variable exponent was studied in [1, 7], and existence of solutions for variable exponent problems was studied in a series of papers [3, 9, 12, 20, 24, 30, 33, 36, 39, 44, 45].”
On a fractional degenerate Kirchhoff-type problem (2017, background): “We also mention, for the sake of completeness, that degenerate Kirchhofftype problems driven by non-homogeneous elliptic operators have been recently taken into account, for instance, in [13, 14, 15, 17, 34, 35].”
Existence of solutions for Kirchhoff type problem involving the non-local fractional p-Laplacian (2015, background): “In [35], the authors established the existence and multiplicity of nontrivial solutions for a Kirchhoff type eigenvalue problem in R involving critical nonlinearity and nonlocal fractional Laplacian, see also [4,36] for further details about this kind of nonlinearity.”
Existence of solutions for perturbed fractional p-Laplacian equations (2016, background): “B. Zhang was supported by Natural Science Foundation of Heilongjiang Province of China (No.”
Double phase anisotropic variational problems and combined effects of reaction and absorption terms (2018, background): “3 of [42]), we have lim n→+∞ ΦA (un) = ΦA (u).”
Ground state solutions of scalar field fractional Schrödinger equations (2015, unknown): “[42]where the open problemgiven in [3]was solved.”
A pocket guide to nonlinear differential equations in Musielak–Orlicz spaces (2018, background): “Since the setting is carefully examined and broad range of problems is already addressed, we mention only a few attempts to basic properties of PDEs such as existence [75, 93, 148, 174], regularity results [1, 2], maximal principle [118], and nonexistence [4, 83].”
On doubly nonlocal fractional elliptic equations (2015, methodology): “See also the relevant contributions [10, 24, 26] where Kirchhoff-type problems have been studied by using different methods and approaches.”
Existence and multiplicity of entire solutions for fractional p-Kirchhoff equations (2016, methodology): “(b) In the case of the Laplacian, we complete the picture of solutions in [29] since (−∆)s becomes −∆ as s → 1−, see [15].”
Multiple solutions for nonhomogeneous Schrödinger–Kirchhoff type equations involving the fractional p-Laplacian in RN\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setl (2015, background): “We refer also to [5,41] for related problems.”