ON A CLASS OF NONLOCAL ELLIPTIC PROBLEMS WITH CRITICAL GROWTH

By Claudianor Oliveira Alves, Francisco Júlio S. A. Corrêa, Giovany M. Figueiredo. 2010

189 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/2faa82a71e8e5e72cde7e31ef55440db0e3c2469

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

Existence and multiplicity of solutions for Kirchhoff type problem with critical exponent (2013, background): “The function g(t) = bt does not satisfy the assumption that g(t) ≥ α > 0 in [20] and [21].”
The critical problem of Kirchhoff type elliptic equations in dimension four (2014, background): “[8]) for the Kirchhoff type equations are observed in [2], [10], [20], [21] and [29].”
A multiplicity result for a fractional Kirchhoff equation in ℝN with a general nonlinearity (2016, background): “r are invariant under rotations, so, from now on, we will directly deﬁne our functionals in Hs rad(R N). Following [20], let χ∈ C∞([0,+∞),R) be a cut-oﬀ function such that χ(t) = 1 for t∈ [0,1] 0 ≤ χ(t) ≤ 1 for t∈ (1,2) χ(t) = 0 for t∈ [2,+∞) kχ′k∞ ≤ 2, and we set ξΛ(u) = χ kuk2 Hs(RN) Λ2 ! . T”
Existence and concentration of positive ground states for a Kirchhoff equation involving critical Sobolev exponent (2014, background): “u ∈ H(1)(R(3)), u > 0, where > 0 is a small parameter, p ∈ [3, 5), a, b are positive constants, μ > 0 is a parameter, and the nonlinear growth of |u|4u reaches the Sobolev critical exponent since 2∗ = 6 for three spatial dimensions.”
Existence of solution for a class of nonlocal elliptic problem via sub-supersolution method (2013, background): “More details about this class of problem can be see in [4], [5], [7], [16], [20] and [21] and their references.”
Multiplicity and concentration behavior of positive solutions for a Schrödinger–Kirchhoff type problem via penalization method (2013, background): “The reader may consult [1], [2], [3], [9], [10], [14], [21] and the references therein, for more informations on nonlocal problems.”
Positive solutions of Kirchhoff type elliptic equations involving a critical Sobolev exponent (2014, background): “Recently some results related to (K1) are obtained in [2,14,15,33].”