The impact of the mountain pass theory in Nonlinear analysis: a mathematical survey

By Patrizia Pucci, Vicentiu D. Rădulescu. 2010

93 citations recorded by the source corpus.

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Citations in the corpus

Mountain Pass solutions for non-local elliptic operators (2012, methodology): “Introduction One of the most celebrated applications of the Mountain Pass Theorem (see [1,5,6,8]) consists in the construction of non-trivial solutions of semilinear equations of the type {− u = f (x,u) inΩ, u = 0 on ∂Ω.”
Multiplicity and concentration of solutions to the nonlinear magnetic Schrödinger equation (2020, background): “Now we show that the functional Jε satisfies the mountain pass geometry (see [9,33,37]).”
Sequences of weak solutions for fractional equations (2013, methodology): “12]) to this kind of equations motivated by the current literature where the MPT has been intensively applied to find solutions to quasilinear elliptic equations; see [2, 10,11,18].”
Existence of infinitely solutions for a modified nonlinear Schrödinger equation via dual approach (2018, background): “[8] M. Ghergu, V. Radulescu; Singular elliptic problems: bifurcation and asymptotic analysis.”
Relations between the mountain pass theorem and local minima (2012, background): “For a complete overview on the mountain pass results and related topics, we refer to the exhaustive works [11], [12] and [15].”
Nonlinear nonhomogeneous singular problems (2019, result): “We also refer to the monograph by Ambrosetti & Prodi [2] for advances related to the mountain pass theory and to the survey by Pucci & Rădulescu [39] on the impact of this in nonlinear analysis.”
Isotropic and anisotropic double-phase problems: old and new (2019, background): “Rădulescu [28] for a survey on the mountain pass theorem.”