Superlinear problems without Ambrosetti and Rabinowitz growth condition

By Olimpio Hiroshi Miyagaki, M. Souto. 2008

228 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/1ddf6d496a11bf7c92f4d6d8a75cc037f79cabe1

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

EXISTENCE OF NONTRIVIAL SOLUTIONS TO POLYHARMONIC EQUATIONS WITH SUBCRITICAL AND CRITICAL EXPONENTIAL GROWTH (2012, background): “[2, 13, 17, 23, 36], the Ambrosetti-Rabinowitz condition played an important role.”
Elliptic Equations and Systems with Subcritical and Critical Exponential Growth Without the Ambrosetti–Rabinowitz Condition (2014, background): “For example , Miyagaki and Souto [32] studied a problem with parameter λ and adapted some monotonicity arguments as in [41] [42].”
On superlinear problems without the Ambrosetti and Rabinowitz condition (2010, methodology): “We refer the readers to Miyagaki and Souto [18, Section 1] for a detailed discussion on the assumptions of [6] [20] [25].”
Relations between the mountain pass theorem and local minima (2012, background): “Very recently, existence results for elliptic Dirichlet problems without (AR) condition have been obtained (see, for instance, [6], [8], [10] and the references therein).”
The existence of a nontrivial solution to a nonlinear elliptic problem of linking type without the Ambrosetti-Rabinowitz condition (2011, unknown): “1 of [14] generalizes the main results of [3, 8, 27] concerning (1.”
N-Laplacian Equations in ℝN with Subcritical and Critical GrowthWithout the Ambrosetti-Rabinowitz Condition (2013, methodology): “This condition was first introduced by Jeanjean [22], and then was used by numerous authors, for example, [38, 31, 41, 47, 49].”
Degenerate Kirchhoff problems involving the fractional p-Laplacian without the (AR) condition (2015, background): “For this reason, in recent years, some researchers have been dedicated to dropping the (AR) condition, see, for example, [18,22–24] for the related discussions.”
Wang’s multiplicity result for superlinear (,)–equations without the Ambrosetti–Rabinowitz condition (2013, methodology): “For an overview of the relevant literature in this direction, we refer to the pioneering papers of Liu–Wang [17] and of Li–Wang–Zeng [14] (where the analogue of H(ii) in Section 3 below was introduced for p = 2), and to the more recent ones of Li–Yang [15], Liu [16] and Miyagaki–Souto [19].”
Infinitely Many Solutions of Superlinear Elliptic Equation (2013, background): “α k ( λ) ≤ ζk ( λ) := inf γ∈Γ k max u∈B k Φ λ (γ (u)) , ∀λ ∈ [1, 2] , (20) where B k = {u ∈ Y k : ‖u‖ ≤ r k } and Γ k := {γ ∈”