Results 1 to 10 of about 2,592,777 (103)
Bifurcation of Gradient Mappings Possessing the Palais-Smale Condition [PDF]
International Journal of Mathematics and Mathematical Sciences, 2011 This paper considers bifurcation at the principal eigenvalue of a class of gradient operators which possess the Palais-Smale condition. The existence of the bifurcation branch and the asymptotic nature of the bifurcation is verified by using the ...
Elliot Tonkes
doaj +2 more sources
A Generalized Palais-Smale Condition in the Fr\'{e}chet space setting
Pracì Mìžnarodnogo Geometričnogo Centru, 2018 The Palais-Smale condition was introduced by Palais and Smale in the mid-sixties and applied to an extension of Morse theory to infinite dimensional Hilbert spaces.
Kaveh Eftekharinasab
doaj +3 more sources
The Solvability of Concave-Convex Quasilinear Elliptic Systems Involving $p$-Laplacian and Critical Sobolev Exponent [PDF]
Sahand Communications in Mathematical Analysis, 2018 In this work, we study the existence of non-trivial multiple solutions for a class of quasilinear elliptic systems equipped with concave-convex nonlinearities and critical growth terms in bounded domains.
Somayeh Khademloo, Saeed Khanjany Ghazi
doaj +1 more source
On variational nonlinear equations with monotone operators
Advances in Nonlinear Analysis, 2020 Using monotonicity methods and some variational argument we consider nonlinear problems which involve monotone potential mappings satisfying condition (S) and their strongly continuous perturbations.
Galewski Marek
doaj +1 more source
Electronic Journal of Differential Equations, 2023 In this article, we consider a singular elliptic problem with singular nonlinearities and critical Caffarelli-Kohn-Nirenberg exponent. By using variational methods and Palais-Smale condition, we show the existence of at least two nontrivial solutions ...
Mohammed El Mokhtar Ould El Mokhtar
doaj +1 more source
Periodic traveling waves in Fermi–Pasta–Ulam type systems with nonlocal interaction on 2d-lattice
Математичні Студії, 2023 The paper deals with the Fermi--Pasta--Ulam type systems that describe an infinite systems of nonlinearly coupled particles with nonlocal interaction on a two dimensional lattice.
S. M. Bak, G. M. Kovtonyuk
doaj +1 more source
Remarks on compactness conditions and their application
Electronic Journal of Differential Equations, 2023 We review typical compactness conditions used in variational techniques and some of their properties, and the relationships between them. In particular, we provide some new insights into results related to the Palais-Smale and Cerami conditions, and ...
David G. Costa
doaj +3 more sources
Existence of Positive Solutions of Semilinear Biharmonic Equations
Abstract and Applied Analysis, 2014 This paper is concerned with the existence of positive solutions of semilinear biharmonic problem whose associated functionals do not satisfy the Palais-Smale condition.
Yajing Zhang, Yinmei Lü, Ningning Wang
doaj +1 more source
Advanced Nonlinear Studies, 2020 In this paper we establish a new critical point theorem for a class of perturbed differentiable functionals without satisfying the Palais–Smale condition.
Bahrouni Anouar +2 more
doaj +1 more source
Advances in Nonlinear Analysis, 2023 The article deals with the existence of a pair of nontrivial nonnegative and nonpositive solutions for a nonlinear weighted quasilinear equation in RN{{\mathbb{R}}}^{N}, which involves a double-phase general variable exponent elliptic operator A{\bf{A}}.
Liu Jingjing, Pucci Patrizia
doaj +1 more source