Three Weak Solutions for Nonlocal Fractional Equations

By Giovanni Molica Bisci, Bruno Antonio Pansera. 2014

53 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/7d21e7a33cfaced693d00bebdac78face3a0bca0

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

Degenerate Kirchhoff problems involving the fractional p-Laplacian without the (AR) condition (2015, background): “The literature on non-local fractional operators and their applications to differential equations is very interesting and quite large, the reader is referred to [14–18] and the references therein, here we just mention a few works.”
Existence of solutions for Kirchhoff type problem involving the non-local fractional p-Laplacian (2015, background): “We refer also to [13,14,29,30,32,40,43,44] for further details on the functional framework and its applications to the existence of solutions for problem (1.”
On a fractional degenerate Kirchhoff-type problem (2017, unknown): “The nonlocal analysis that we perform here is quite general and exploited for other goals in several recent contributions; see [26, 27, 28, 31, 32].”
Ground state solutions of scalar field fractional Schrödinger equations (2015, methodology): “Remark 7 For completenesswe justmention here that, by using a variational approach similar to the one adopted here, in [36–38] the authors proved the existence and the multiplicity of weak solutions for nonlocal problems involving regional fractional Laplacian operators in a suitable abstract settin”
On doubly nonlocal fractional elliptic equations (2015, methodology): “Indeed, the nonlocal analysis which we perform in this paper in order to use the Mountain Pass Theorem is quite general and it was successfully exploited for other goals in several recent contributions (see [16, 19, 20, 21, 23, 28, 30, 31, 32] and [15] for various properties on the fractional Sobole”
Fractional Sobolev spaces with variable exponents and fractional p(x)-Laplacians (2017, background): “In the constant exponent case it is known as the fractional p-Laplacian, see [2, 3, 5, 7, 8, 9, 11, 12, 15, 16, 17] and references therein.”
Multiplicity results for the non-homogeneous fractional p-Kirchhoff equations with concave–convex nonlinearities (2015, background): “The literature on fractional operators and their applications is very huge, here we just mention a few, see for example [10–20], especially [21] and [22,23] for two different fractional Laplacian involving concave–convex nonlinearities.”
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): “The literature on fractional and nonlocal operators and on their applications is very interesting and quite large, we refer the readers to [5,6,13,14,23,24,36–38,43,44,46,49,50] and the references therein.”
Infinitely many solutions for a fractional Kirchhoff type problem via Fountain Theorem (2015, unknown): “6), see for example [16,17,28,29,26,35,34,42,43].”