Nontrivial critical groups in $p$-Laplacian problems via the Yang index

By Kanishka Perera. 2003

122 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Orthopedics and Sports Medicine

View Paper: https://www.semanticscholar.org/paper/2262be58603eebc6d024f6a4a665dc56c3642a96

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In Applied Mathematics

In Computational Theory and Mathematics

In Orthopedics and Sports Medicine

Citations in the corpus

On superlinear problems without the Ambrosetti and Rabinowitz condition (2010, background): “As in Perera [19], base on our computation of C .”
Existence results for fractional p-Laplacian problems via Morse theory (2014, methodology): “This type of construction was introduced for the p-Laplacian by Perera [33] (see also Perera & Szulkin [36]), and it is slightly different from the”
(N,q)‐Laplacian problems with critical Trudinger‐Moser nonlinearities (2014, methodology): “1, so we will use the following scheme based on the cohomological index as in Perera [19].”
On ground states of superlinear p-Laplacian equations in RN (2010, background): “On the other hand, the quasilinear case is usually considered on a bounded domain, the reader may find some results in this direction in [4,7,9,21, 24 ].”
Nontrivial Solutions for p-Laplace Equations with Right-Hand Side Having p-Linear Growth at Infinity (2005, background): “It is also possible to define, in at least three different ways, a diverging sequence (λ n ) of eigenvalues (see Drabek and Robinson, 1999 ; Perera, 2003a and Section.”
Linking over cones and nontrivial solutions for p-Laplace equations with p-superlinear nonlinearity (2007, background): “It is also possible to define, in at least three different variational ways, a diverging sequence (λm) in σ(− p) (see [18,13,26,7,27]), but it is not known if these definitions are equivalent for m 3, if the whole set σ(− p) is covered and if there exists an induced direct sum decomposition.”
Morse Theoretic Aspects of $p$-Laplacian Type Operators (2010, methodology): “We will work with a new sequence of eigenvalues introduced by the first author in [98] that uses the Z2-cohomological index of Fadell and Rabinowitz.”
The Brezis–Nirenberg problem for the fractional p-Laplacian (2015, methodology): “ necessary for our purposes here, so we will use the following 4 S. MOSCONI, K. PERERA, M. SQUASSINA, AND Y. YANG scheme based on the cohomological index as in Iannizzotto et al.[28] (see also Perera [36]). Let Ψ(u) = 1 |u|p p , u ∈ M = u ∈ Ws,p 0 (Ω) : kuk = 1 . Then eigenvalues of problem (1.4) co”
Linking solutions for p-Laplace equations with nonlinearity at critical growth (2009, result): “LINKING SOLUTIONS 5 In order to state our results in the line of (b), let us set, according to [6, 7, 17, 18],”