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A Critical Concave–Convex Kirchhoff-Type Equation in $$\mathbb R^4$$ Involving Potentials Which May Vanish at Infinity
- Source :
- Annales Henri Poincaré. 23:25-47
- Publication Year :
- 2021
- Publisher :
- Springer Science and Business Media LLC, 2021.
-
Abstract
- We establish the existence and multiplicity of solutions for a Kirchhoff-type problem in $$\mathbb R^4$$ involving a critical and concave–convex nonlinearity. Since in dimension four, the Sobolev critical exponent is $$2^*=4$$ , there is a tie between the growth of the nonlocal term and the critical nonlinearity. This turns out to be a challenge to study our problem from the variational point of view. Some of the main tools used in this paper are the mountain-pass and Ekeland’s theorems, Lions’ Concentration Compactness Principle and an extension to $$\mathbb R^N$$ of the Struwe’s global compactness theorem.
- Subjects :
- Nuclear and High Energy Physics
Dimension (graph theory)
Mathematical analysis
Vanish at infinity
Mathematics::Analysis of PDEs
Regular polygon
Statistical and Nonlinear Physics
Sobolev space
Nonlinear system
Compact space
Compactness theorem
Critical exponent
Mathematical Physics
Mathematics
Subjects
Details
- ISSN :
- 14240661 and 14240637
- Volume :
- 23
- Database :
- OpenAIRE
- Journal :
- Annales Henri Poincaré
- Accession number :
- edsair.doi...........ecdd07b0dafe3affa6d88c3f9aeaf220