Journal
APPLICABLE ANALYSIS
Volume 101, Issue 2, Pages 421-436Publisher
TAYLOR & FRANCIS LTD
DOI: 10.1080/00036811.2020.1745778
Keywords
Nonhomogeneous elliptic problem; Kirchhoff-type problem; critical exponential growth; Trudinger-Moser inequality
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Funding
- National Natural Science Foundation of China [11971392]
- Fundamental Research Funds for the Central Universities
- Natural Science Foundation of Chongqing, China [cstc2019jcyjjqX0022]
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In this article, the Ekeland variational principle, mountain pass theorem, and Trudinger-Moser inequality are used to establish the existence and multiplicity of solutions for a nonhomogeneous Kirchhoff-type elliptic problem.
In this article, the Ekeland variational principle, mountain pass theorem and Trudinger-Moser inequality are applied to establish the existence and multiplicity of solutions for the following nonhomogeneous Kirchhoff-type elliptic problem: -m(integral(Omega)vertical bar del u vertical bar(2) dx) Delta u = f (x, u) + epsilon h(x) in Omega; u = 0 on partial derivative Omega, where Omega is a smooth bounded domain in R-2, m : R+ -> R+ is a Kirchhoff function, f : Omega x R. R is a continuous function, h epsilon (W-0(1,2) (Omega)) * = W--1,W-2, h = 0, h not equivalent to 0, and epsilon is a small positive parameter. The nonlinearity term f (x, s) behaves like e(alpha 0s2) when vertical bar s vertical bar -> infinity for some alpha(0) > 0.
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