Sobolev-Type Spaces on the Dual of the Chébli-Trimèche Hypergroup and Applications by Mourad Jelassi, Hatem Mejjaoli

“…Some properties are given; in particular we establish a compactness-type imbedding result which allows a Reillich-type theorem. Next, we introduce a generalized Weierstrass transform and, using the theory of reproducing kernels, some applications are given.…”
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Subharmonic Solutions of Nonautonomous Second Order Differential Equations with Singular Nonlinearities by N. Daoudi-Merzagui, F. Derrab, A. Boucherif

“…Our approach is based on a variational method, in particular the saddle point theorem.…”
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On Convergence of the Explicit Difference Scheme for Evolution Variational Inequality with Nonlocal Space Operator by O.V. Glazyrina, M.F. Pavlova

“…Conditions of stability for the constructed difference scheme are obtained. The theorem of convergence is proved under minimal assumptions on the smoothness of the original data.…”
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Existence and Uniqueness of Positive Solitons for a Second-Order Difference Equation by Xinfu Li, Guang Zhang, Ying Wang

“…To this end, the Dirichlet eigenvalue problem with positive and negative coefficients is considered, and a general sub- and upper-solution theorem is also obtained.…”
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Quasiperiodic Solutions of Completely Resonant Wave Equations with Quasiperiodic Forced Terms by Yixian Gao, Weipeng Zhang, Jing Chang

“…The proofs are based on the variational Lyapunov-Schmidt reduction and the linking theorem, while the bifurcation equations are solved by variational methods.…”
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Analytical Approaches on the Attractivity of Solutions for Multiterm Fractional Functional Evolution Equations by Xiangling Li, Azmat Ullah Khan Niazi, Farva Hafeez, Reny George, Azhar Hussain

“…In this respect, we use a familiar Schauder’s fixed-point theorem (SFPT) related to the method of measure of noncompactness (MNC). …”
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Infinitely Many Sign-Changing Solutions for Some Nonlinear Fourth-Order Beam Equations by Ying Wu, Guodong Han

“…Several new existence theorems on positive, negative, and sign-changing solutions for the following fourth-order beam equation are obtained: u(4)=f(t,u(t)),   t∈[0,1];  u(0)=u(1)=u′′(0)=u′′(1)=0, where f∈C([0,1]×ℝ1,ℝ1). …”
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On the Approximation of Generalized Lipschitz Function by Euler Means of Conjugate Series of Fourier Series by Jitendra Kumar Kushwaha

“…The present study deals with a new theorem on the approximation of functions of Lipschitz class by using Euler’s mean of conjugate series of Fourier series. …”
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Investigating a Class of Generalized Caputo-Type Fractional Integro-Differential Equations by Saeed M. Ali, Wasfi Shatanawi, Mohammed D. Kassim, Mohammed S. Abdo, S. Saleh

“…Our approach is based on Babenko’s technique, Banach’s fixed point theorem, and Banach’s space of absolutely continuous functions. …”
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Cocompact Open Sets and Continuity by Samer Al Ghour, Salti Samarah

“…As a main result, a decomposition theorem of continuity is obtained.…”
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Periodicity in a ratio-dependent predator-prey system with stage structure for predator by Fengde Chen

“…With the help of a continuation theorem based on Gaines and Mawhin's coincidence degree, easily verifiable criteria are established for the global existence of positive periodic solutions of a delayed ratio-dependent predator-prey system with stage structure for predator. …”
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Multiplicity of Quasilinear Schrödinger Equation by Xiaorong Luo, Anmin Mao, Xiangxiang Wang

“…When the pair of parameters belongs to a certain subset of ℝ2, we establish the existence of a nontrivial mountain pass-type solution and infinitely many negative energy solutions by using some new techniques and dual fountain theorem. Recent results from the literature are improved and extended.…”
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Discontinuous Sturm-Liouville Problems and Associated Sampling Theories by M. M. Tharwat

“…We closely follow the analysis derived by Fulton (1977) to establish the needed relations for the derivations of the sampling theorems including the construction of Green's function as well as the eigenfunction expansion theorem. …”
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The continuous Jacobi transform by E. Y. Deeba, E. L. Koh

“…The basic properties including the inversion theorem for the continuous Jacobi transform are studied. …”
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Dynamic Analysis of a Model for Spruce Budworm Populations with Delay by Ahmadjan Muhammadhaji, Azhar Halik

“…By using the inequality techniques, continuation theorem, and the construction of suitable Lyapunov functional, we establish a set of easily verifiable sufficient conditions on the permanence, existence, and global attractivity of positive periodic solutions for the considered system. …”
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Hamilton-Jacobi Method for Mechanical Systems on Time Scales by Xiang-Hua Zhai, Yi Zhang

“…By choosing an appropriate generating function, we construct the Hamilton-Jacobi equation on time scales and prove the Jacobi theorem on time scales. An example for an Emden-Fowler type equation is discussed to show the application of the method.…”
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A Rosenzweig-MacArthur (1963) Criterion for the Chemostat by Torsten Lindström, Yuanji Cheng

“…In this paper we use the implicit function theorem and implicit derivatives for proving that a similar graphical criterion holds under chemostat conditions, too.…”
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Distributed Optimization of Multiagent Systems in Directed Networks with Time-Varying Delay by Junxiu Yan, Hui Yu

“…Different from most ways of solving distributed optimization problem, the Lyapunov-Razumikhin theorem is applied to the convergence analysis instead of the Lyapunov-Krasovskii functionals with LMI conditions. …”
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Existence and Exponential Stability of Periodic Solution for a Class of Generalized Neural Networks with Arbitrary Delays by Yimin Zhang, Yongkun Li, Kuohui Ye

“…By the continuation theorem of coincidence degree and M-matrix theory, we obtain some sufficient conditions for the existence and exponential stability of periodic solutions for a class of generalized neural networks with arbitrary delays, which are milder and less restrictive than those of previous known criteria. …”
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Blow-Up Solutions for a Singular Nonlinear Hadamard Fractional Boundary Value Problem by Imed Bachar, Said Mesloub

“…Using properties of Green’s function and a fixed point theorem, we show that the problem has positive solutions which blow up. …”
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