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Some Abstract Critical Point Theorems and Applications in Wave Equations
With the index defined in [J. Differential Equations, 2016, 260(4): 3749–3784] and [Front. Math., 2023, 18(3): 731–742], we get some critical point...
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Real Normal Form of a Binary Polynomial at a Second-Order Critical Point
AbstractA real polynomial in two variables is considered. Its expansion near the zero critical point begins with a third-degree form. The simplest...
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Fixed point–critical point hybrid theorems and application to systems with partial variational structure
In this paper, fixed point arguments and a critical point technique are combined leading to hybrid existence results for a system of two operator...
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On the Number of Limit Cycles of Planar Piecewise Smooth Quadratic Systems with Focus-Parabolic Type Critical Point
In this paper we investigate the number of small amplitude limit cycles bifurcated from a class of planar piecewise smooth quadratic systems with...
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Microscopic derivation of Ginzburg–Landau theory and the BCS critical temperature shift in general external fields
We consider the Bardeen–Cooper–Schrieffer (BCS) free energy functional with weak and macroscopic external electric and magnetic fields and derive the...
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Conformal Radius Has Unique Critical Point when Pre-Schwarzian Derivative is Subordinate to Classical Majorants
AbstractWe obtain a number of the uniqueness criteria for the critical point of the conformal radius in the form of the subordination of...
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Desargues’s Perspective Theory: A Critical Interpretation of the Fundamental Theorem
This short essay gets to the heart of the debate that arose about the upper part of Table 151 of the Manière universelle , written by Abraham Bosse...
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Nonsmooth critical point theory and applications to the spectral graph theory
Existing critical point theories including metric and topological critical point theories are difficult to be applied directly to some concrete...
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Planar Equilibrium Measure Problem in the Quadratic Fields with a Point Charge
We consider a two-dimensional equilibrium measure problem under the presence of quadratic potentials with a point charge and derive the explicit...
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Von Neumann, Morgenstern, and Theory of Games: Critical Reassessment of Zero-Sum Games
This chapter gives a brief yet critical account of the theory of games as jointly developed by the two superstars in the twentieth century; namely,...
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A Schrödinger–Poisson System with the Critical Growth on the First Heisenberg Group
AbstractIn this paper, we study the Schrödinger–Poisson system with the critical growth on the first Heisenberg group. With the aid of the Green’s...
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An abstract critical point theorem with applications to elliptic problems with combined nonlinearities
We prove an abstract critical point theorem based on a cohomological index theory that produces pairs of nontrivial critical points with nontrivial...
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Critical Point Theory Sandwich and Linking Systems
This monograph collects cutting-edge results and techniques for solving nonlinear partial differential equations using critical points. Including...
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Critical Points of Potential Functions and Floer Cohomology
In this chapter, with the analysis of one-point open Gromov–Witten invariants given in the previous section at our disposal, we develop the critical...
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Ground state solution for the nonlinear Klein–Gordon equation coupled with Born–Infeld theory with critical exponents
In this paper, we study the existence of ground state solution for nonlinear Klein–Gordon equation coupled with Born–Infeld theory when the...
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Proximal Point Method for Quasiconvex Functions in Riemannian Manifolds
This paper studies the convergence of the proximal point method for quasiconvex functions in finite dimensional complete Riemannian manifolds. We...
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Existence and multiplicity of solutions for three-point boundary value problems with instantaneous and noninstantaneous impulses
In this paper, three-point boundary value problems for second-order p -Laplacian differential equations with instantaneous and noninstantaneous...
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Multiparameter discrete Morse theory
The main objective of this paper is to extend Morse–Forman theory to vector-valued functions. This is mostly motivated by the need to develop new...
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Upper bounds for the number of isolated critical points via the Thom–Milnor theorem
We apply the Thom–Milnor theorem to obtain the upper bounds on the amount of isolated (1) critical points of a potential generated by several fixed...