On the critical $p$-Kirchhoff equation
Copyright policy )On the critical $p$-Kirchhoff equation
We study a nonlocal elliptic equation of $p$-Kirchhoff type involving the critical Sobolev exponent. First we give sufficient conditions for the $(\text{PS})$ condition to hold. Then we prove some existence and multiplicity results using tools from Morse theory, in particular, the notion of a cohomological local splitting and eigenvalues based on the Fadell-Rabinowitz cohomological index.
- Florida Institute of Technology United States
existence, Existence problems for PDEs: global existence, local existence, non-existence, \(p\)-Kirchhoff-type equation, Primary 35J92, Secondary 35B33, 58E05, Critical exponents in context of PDEs, Mathematics - Analysis of PDEs, critical Sobolev exponent, FOS: Mathematics, multiplicity, Morse theory, Quasilinear elliptic equations with \(p\)-Laplacian, Analysis of PDEs (math.AP)
existence, Existence problems for PDEs: global existence, local existence, non-existence, \(p\)-Kirchhoff-type equation, Primary 35J92, Secondary 35B33, 58E05, Critical exponents in context of PDEs, Mathematics - Analysis of PDEs, critical Sobolev exponent, FOS: Mathematics, multiplicity, Morse theory, Quasilinear elliptic equations with \(p\)-Laplacian, Analysis of PDEs (math.AP)
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