Existence results for double-phase problems via Morse theory

By Kanishka Perera, Marco Squassina. 2016

116 citations recorded by the source corpus.

We obtain nontrivial solutions for a class of double-phase problems using Morse theory. In the absence of a direct sum decomposition, we use a cohomological local splitting to get an estimate of the critical groups at zero.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/d262fc27cc68bcc449ece8dde6cbbfc5eee63da0

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

A new class of double phase variable exponent problems: Existence and uniqueness (2021, methodology): “Perera-Squassina [59] showed the existence of a solution by applying Morse theory where they used a cohomological local splitting to get an estimate of the critical groups at zero.”
An existence result for singular Finsler double phase problems (2020, result): “Recent existence results for double phase problems in the case if F is the Euclidean norm and without singular term can be found, for example, in the papers of Colasuonno-Squassina [11], Liu-Dai [30], Gasiński-Papageorgiou [24], Gasiński-Winkert [25–27], Perera-Squassina [41] and the references ther”
Existence and uniqueness results for double phase problems with convection term (2019, background): “Recently, Perera-Squassina [27] studied double phase problems and stated an existence result which was proved via Morse theory in terms of critical groups.”
Existence of solutions for double phase obstacle problems with multivalued convection term (2020, background): “4], Gasiński-Winkert [16], Liu-Dai [20], Perera-Squassina [27] and problems with other general differential operator and a convection term by Gasiński-Papageorgiou [14].”
New embedding results for double phase problems with variable exponents and a priori bounds for corresponding generalized double phase problems (2022, methodology): “We refer to the papers of Bahrouni-R˘adulescu–Winkert [3] (Baouendi–Grushin operator), Colasuonno–Squassina [15] (double phase eigenvalue problems), Farkas–Winkert [31] (Finsler double phase problems), Gasi´nski-Papageorgiou [32] (locally Lipschitz right-hand sides), Gasi´nski–Winkert [34, 35] (conv”
Sign changing solution for a double phase problem with nonlinear boundary condition via the Nehari manifold (2020, background): “Perera-Squassina [40] showed the existence of a solution of problem (1.”
On double phase Kirchhoff problems with singular nonlinearity (2021, unknown): “We refer to the papers of Arora-Shmarev [2, 3] (parabolic double phase problems), Colasuonno-Squassina [7] (eigenvalue problems), Farkas-Winkert [14], Farkas-Fiscella-Winkert [13] (singular Finsler double phase problems), Fiscella [15] (Hardy potentials), Gasiński-Papageorgiou [19] (locally Lipschit”