Existence, Uniqueness, and Input-to-State Stability of Ground State Stationary Strong Solution of a Single-Species Model via Mountain Pass Lemma [PDF]
Complexity, 2021 In this study, the authors utilize mountain pass lemma, variational methods, regularization technique, and the Lyapunov function method to derive the unique existence of the positive classical stationary solution of a single-species ecosystem ...
Ruofeng Rao, Quanxin Zhu, Jialin Huang
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On mountain pass theorem and its application to periodic solutions of some nonlinear discrete systems [PDF]
Advances in Difference Equations, 2019 In this paper, we prove a new quantitative deformation lemma, and then gain a new mountain pass theorem in Hilbert spaces. By using the new mountain pass theorem, we obtain the new existence of two nontrivial periodic solutions for a class of nonlinear ...
Liang Ding, Jinlong Wei, Shiqing Zhang
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A generalized mountain pass lemma with a closed subset for locally Lipschitz functionals [PDF]
Applicable Analysis, 2021 arXiv admin note: text overlap with arXiv:1405 ...
Li, Fengying +2 more
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Mountain pass lemma and new periodic solutions of the singular second order Hamiltonian system [PDF]
Boundary Value Problems, 2014 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Li, Bingyu, Li, Fengying
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A bounded mountain pass lemma without the (PS) condition and applications [PDF]
Transactions of the American Mathematical Society, 1992 The author's generalization of the fundamental mountain pass lemma is the following: Theorem. Let \(G(u)\in C^ 1(H,R^ 1)\), \(u_ k\) converging weakly to \(u\), \(| G(u_ k)|\leq c\), \(G'(u_ k)\to 0\), imply that \(G'(u)=0\). Assume that \(H=N\oplus M\), \(\dim N0\), such that \[ c_ 0\equiv\max_{bdy\{v\in N\mid\| v\|\leq R_ 0\}}G0 ...
M. Schechter
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Symmetric mountain pass lemma and sublinear elliptic equations
Journal of Differential Equations, 2016 This paper deals with the qualitative analysis of solutions of a class of quasilinear elliptic equations with Dirichlet zero boundary condition. The main result of this paper establishes a necessary and sufficient condition such that the zero solution is an accumulation point of the set of all solutions.
R. Kajikiya
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ON A NEW FIXED POINT THEOREM ON HILBERT SPACES VIA THE MOUNTAIN PASS LEMMA AND APPLICATIONS TO ELLIPTIC BOUNDARY VALUE PROBLEMS [PDF]
International Journal of Pure and Apllied Mathematics, 2016 In this paper we present a new fixed point theorem in Hilbert spaces. Using a suitable critical point theorem we provide conditions under which potential operators have a fixed point. An application is given to illustrate the theory.
A. Souad, T. Moussaoui, D. O'Regan
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Some extensions of the mountain pass lemma
Differential and Integral Equations, 1988 This article deals with some variants of the classical mountain pass lemma. In the first part the following result is obtained: if \(f: \mathbb{E}\to\mathbb{R}\) is a \(C^ 1\) smooth functional with \(PS\)-condition on a real Banach space \(\mathbb{E}\), \(x_ 0,x_ 1\in\mathbb{E}\), \({\mathcal D}\) is an open neighborhood, \(x_ 0,x_ 1\not\in{\mathcal D}
Guo, Da Jun, Sun, Jing Xian, Qi, Gui Jie
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An extension of the mountain pass lemma
Applied Mathematics Letters, 2008 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wang, Lizhou, Li, Dongsheng
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Journal of Functional Analysis, 2005 In this paper it is proved a critical point theorem of mountain-pass type which yields a sequence of critical points converging to zero. The proof combines a pseudo-gradient property with a deformation lemma. The abstract result is applied for proving a multiplicity result for the semilinear elliptic equation \(-\Delta u=f(x,u)\) in \(\Omega\) under ...
R. Kajikiya
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