The structure of the critical set in the mountain-pass theorem for nondifferentiable functions
Differential and Integral Equations, 2003 The paper studies the structure of the critical set at the level given by the minimax value in the mountain pass theorem for nonsmooth functionals expressed as a sum of a locally Lipschitz function and a proper, convex, lower semicontinuous function on a Banach space.
BARLETTA G, MARANO, Salvatore Angelo
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Transport Pathways of Ozone in Beijing–Tianjin–Hebei Based on Causal Networks
Meteorological Applications, Volume 33, Issue 2, March/April 2026.Applying convergent cross‐mapping and complex network methods, multi‐year, summer and winter O3 concentration transport network models were constructed based on the causal relationship between stations, and it was found that O3 transport in the Beijing–Tianjin–Hebei region was significantly affected by O3 concentration, meteorology, and station ...
Zhen Song +6 more
wiley +1 more source
Three nontrivial solutions for nonlinear fractional Laplacian equations
Advances in Nonlinear Analysis, 2018 We study a Dirichlet-type boundary value problem for a pseudodifferential equation driven by the fractional Laplacian, proving the existence of three non-zero solutions.
Düzgün Fatma Gamze +1 more
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A mountain pass theorem for minimal hypersurfaces with fixed boundary [PDF]
Calculus of Variations and Partial Differential Equations, 2020 In this work, we prove the existence of a third embedded minimal hypersurface spanning a closed submanifold $γ$ contained in the boundary of a compact Riemannian manifold with convex boundary, when it is known a priori the existence of two strictly stable minimal hypersurfaces that bound $γ$.
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Methodological Frameworks for Computational Electrocatalysis: From Theory to Practice
Small Methods, Volume 10, Issue 5, 9 March 2026.Computational modeling is widely used to investigate electrocatalytic reactions, yet accurately describing electrochemical interfaces remains challenging. This review outlines theoretical and computational strategies, based on density functional theory, to model reaction thermodynamics, solvation effects, applied bias, and kinetics.
Michele Re Fiorentin +8 more
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Deformation Lemma, Ljusternik-Schnirellmann Theory and Mountain Pass Theorem on C1-Finsler Manifolds [PDF]
, 1995 ∗Partially supported by Grant MM409/94 Of the Ministy of Science and Education, Bulgaria. ∗∗Partially supported by Grant MM442/94 of the Ministy of Science and Education, Bulgaria.Let M be a complete C1−Finsler manifold without boundary and f : M → R be ...
Tsachev, Tsvetomir +2 more
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An existence theorem of Nontrivial Solutions of Semilinear Equations in Reflexive Banach Spaces and Its Applications [PDF]
, 1996 In this paper, an existence theorem is obtained for nontrival solutions of semilinear equations in reflexive Banach spaces with the duality technique in infinite-dimensional spaces and the nonsmooth mountain pass theorem, a new existence theorem is then ...
Chun-Lei Tang, Tang, Chun-Lei
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Existence of nontrivial solutions for a class of elliptic systems
Electronic Journal of Differential Equations, 2013 Using a version of the generalized mountain pass theorem, we obtain the existence of nontrivial solutions for a class of superquadratic elliptic systems.
Chun Li, Zeng-Qi Ou, Chun-Lei Tang
doaj
Geometric description of the mountain pass critical points [PDF]
, 2014 In this short commentary I present the main results contained in the famous paper [P. Pucci & J. Serrin, The structure of the critical set in the mountain pass theorem, Trans. Amer. Math. Soc. 299 (1987), no. 1, 115–132].
PUCCI, Patrizia
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Existence of Multiple Solutions for a Class of Biharmonic Equations
Discrete Dynamics in Nature and Society, 2013 By a symmetric Mountain Pass Theorem, a class of biharmonic equations with Navier type boundary value at the resonant and nonresonant case are discussed, and infinitely many solutions of the equations are obtained.
Chunhan Liu, Jianguo Wang
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