[PDF] Top 20 Critical Point Theorems and Ekeland Type Variational Principle with Applications

... 19 L.-J. Lin, C.-S. Chuang, and S.-Y. Wang, “From quasivariational inclusion problems to Stampacchia vector quasiequilibrium problems, Stampacchia set-valued vector Ekeland’s variational principle and ... See full document

... new critical point theorems for nonlinear dynamical systems which are generalizations of Dancˇs-Heged ¨us-Medvegyev’s principle in uniform spaces and metric spaces by applying an abstract ... See full document

... By using a Dane˘s’ drop theorem in locally convex spaces we obtain a vectorial form of Ekeland- type variational principle in locally convex spaces. From this theorem, we derive some versions ... See full document

... many applications in op- timization, nonlinear analysis, mathematical economy and mathematical ...fixed point theorem [, ] and nonconvex min- imization theorem according to Takahashi ...Ekeland’s ... See full document

... fixed point the- orems [, –] for a pseudo-metric space ...Brezis-Browder principle, we give generalized Caristi’s fixed point theorems for set-valued maps and de- rive some ...an ... See full document

... recent critical point theorem in [] by considering Zhong’s Ekeland variational ...Palais-Smale type introduced by Cerami ...the critical point ... See full document

... the Ekeland variational principle, the mountain pass theorem, and the saddle point theorem in critical point theory, and by applying the local linking theorem and the saddle ... See full document

... 1974, Ekeland proposed a variational principle, which is the basis of modern variational calculus and has applications in many branches of mathematics, including optimization and fixed ... See full document

... maximality principle is formulated and proved see Section 3. As applications, in cone uniform spaces with the families of generalized pseudodistances, the general variational principle of ... See full document

... our variational principles with Caristi–Kirk type fixed point theorem for multi-valued maps, Takahashi’s minimization theorem, and some other related ...As applications of our results, we ... See full document

... fixed point theorems and coincidence point theorems in the generating space of a quasi-metric ...generalized Ekeland variational principle, and a general ... See full document

... Proof. It may be completed following Reich 30 and ´ Ciri´c 36 and using Corollary 4.5. However, for the sake of completeness, we give an outline of the same. Let t a 2b 2c. For p ∈ 0, 1; define a single-valued map g : Y ... See full document

... [23] Y. Wu, T. Q. An, “Infinitely many solutions for a class of semilinear elliptic equations,” J. Math. Anal. Appl., vol.414, no.1, 285-295, 2014. [24] M. Q. Xiang, B. L. Zhang, M. Ferrara, “Existence of solutions for ... See full document

... Let H be a Hilbert space such that H = V ⊕ W , where V and W are two closed subspaces of H. We generalize an abstract theorem due to Lazer et al. (1975) and a theorem given by Moussaoui (1990-1991) to the case where V ... See full document

... Based on the recent work of random metric theory, namely the Ekeland variational principle on a complete random metric space, this paper studies the Daneš theorem in a complete random normed module. ... See full document

... , which implies that T is an α-η-GF-contraction mapping. Hence, all conditions of Theo- rem . hold true and T has a fixed point. If Fix(T) ⊆ O(z), then α(x, y) ≥ η(x, y) for all x, y ∈ Fix(T ) and so from ... See full document

... Next, we will prove that x is also a fixed point of T. Let K be the minimal subset of C with respect to being nonempty, closed, convex and satisfying the property ( ω ). From the proof of Lemma 4.1, we have x Î K. ... See full document

... One of the most interesting extensions of distance function was reported by Matthews [] by introducing the notion of a partial metric in which self-distance need not be zero. In this celebrated report, Matthews [] ... See full document

... Fixed point theory has played important roles in traditional equilibrium theory, varia- tional inequalities and optimization theory (see ...Fixed point theorems have been applied in the proofs of the ... See full document

... fixed point theorem on complete metric spaces which generalizes the Banach contraction ...principle. Ekeland [3] also obtained a non- convex minimization theorem, often called the ε ... See full document