FIRST AND SECOND-ORDER OP TIMALITY CONDITIONS USING APPROXIMATIONS FOR VECTOR EQUILIBRIUM PROBLEMS WITH CONSTRAINTS by Phan Quốc Khánh, Lê Thanh Tùng

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Global compact attractors and complete bounded trajectories for compressible magnetohydrodynamic system of equations by Muhammad Jan

Subjects: “…weak solutions…”
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On a Class of Anisotropic Nonlinear Elliptic Equations with Variable Exponent by Guoqing Zhang, Hongtao Zhang

“…Furthermore, we also obtain that the weak solution is locally bounded and regular; that is, the weak solution is Lloc∞(Ω) and C1,α(Ω).…”
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Existence of Solutions for Superlinear Second-Order System with Noninstantaneous Impulses by Yucheng Bu

“…Variational methods are used in order to establish the existence of nontrivial weak solution for superlinear second-order system with noninstantaneous impulses. …”
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Stability Analysis of the Supercritical Surface Quasi-Geostrophic Equation by Yan Jia, Xingguo Gui, Bo-Qing Dong

“…Supposing that the weak solution of the surface quasi-geostrophic equation with the force satisfies the growth condition in the critical BMO space , it is proved that every perturbed weak solution converges asymptotically to solution of the original surface quasi-geostrophic equation. …”
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The 2D Dirichlet Problem for the Propagative Helmholtz Equation in an Exterior Domain with Cracks and Singularities at the Edges by P. A. Krutitskii

“…The asymptotic formulae describing singularities of a solution gradient at the edges (endpoints) of the cracks are presented. The weak solution to the problem may not exist, since the problem is studied under such conditions that do not ensure existence of a weak solution.…”
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A frictional contact problem with normal damped response conditions and thermal effects for a thermo-electro-viscoelastic material by Abdelmoumene Djabi

“…The author establishes the existence of a unique weak solution to the problem by utilizing classical results for evolutionary quasivariational elliptic inequalities, parabolic differential equations and fixed point arguments. …”
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A Nonlinear Fractional Problem with a Second Kind Integral Condition for Time-Fractional Partial Differential Equation by Benbrahim Abdelouahab, Taki-Eddine Oussaeif, Adel Ouannas, Khaled M. Saad, Hadi Jahanshahi, Ahmed Diar, Awad M. Aljuaid, Ayman A. Aly

“…The aim of this research is to demonstrate the existence and the uniqueness of the weak solution for a semilinear fractional parabolic problem with the special case of the second integral boundary condition. …”
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Evolutionary variational inequalities arising in quasistatic frictional contact problems for elastic materials by Dumitru Motreanu, Mircea Sofonea

“…For these two problems we prove the existence, the uniqueness and the Lipschitz continuous dependence of the weak solution with respect to the data.…”
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Flow of electrorheological fluid under conditions of slip on the boundary

“…A theorem of existence of a weak solution is proved. For this purpose the approximating-topological method is used.…”
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A Nonhomogeneous Dirichlet Problem for a Nonlinear Pseudoparabolic Equation Arising in the Flow of Second-Grade Fluid by Le Thi Phuong Ngoc, Truong Thi Nhan, Nguyen Thanh Long

“…In Part 1, we use the Galerkin method and compactness method to prove the existence of a unique weak solution of the problem above on (0,T), for every T>0. …”
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On a Class of Schrödinger System Problem in Orlicz–Sobolev Spaces by H. El-Houari, L. S. Chadli, H. Moussa

“…Using the mountain pass theorem, we obtain the existence of a nontrivial and nonnegative weak solution of a quasi-linear Schrödinger system driven by the ω⋅-Laplacian operator in Orlicz–Sobolev spaces.…”
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Optimal Convergence Rates for Solutions of the Monopolar Non-Newtonian Flows by Zhi-qiang Luo

“…By using the energy methods, the perturbed weak solution of perturbed system asymptotically converges to the solution of the original system with the optimal rates (1+t)-1/4.…”
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Remarks on the Pressure Regularity Criterion of the Micropolar Fluid Equations in Multiplier Spaces by Fengjun Guo

“…This study is devoted to investigating the regularity criterion of weak solutions of the micropolar fluid equations in . …”
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The Existence of Solutions to the Nonhomogeneous A-Harmonic Equations with Variable Exponent by Haiyu Wen

“…We first discuss the existence and uniqueness of weak solution for the obstacle problem of the nonhomogeneous A-harmonic equation with variable exponent, and then we obtain the existence of the solutions of the equation d⋆A(x,dω)=B(x,dω) in the weighted variable exponent Sobolev space Wdp(x)(Ω,Λl,μ).…”
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A Capacity Associated with the Weighted Lebesgue Space and Its Applications by Guoliang Li, Guanglan Wang, Lei Zhang

“…More properties of that capacity are explored, and applications to a trace inequality for the weak solution of the equation are considered.…”
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Some Remarks on Biharmonic Elliptic Problems with a Singular Nonlinearity by Baishun Lai

“…In the extremal case λ=λ*, we prove the existence of a weak solution which is the unique solution even in a very weak sense. …”
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On the Stochastic 3D Navier-Stokes-α Model of Fluids Turbulence by Gabriel Deugoue, Mamadou Sango

“…The adequate notion of solutions is that of probabilistic weak solution. We establish the existence of a such of solution. …”
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Existence Theorem for Noninstantaneous Impulsive Evolution Equations by Gul I Hina Aslam, Amjad Ali, Maimona Rafiq

“…The existence and uniqueness of the weak solution of the problem is obtained. In future, this constructive theory can be used for the corresponding semilinear problems.…”
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The Cauchy Problem for the Incompressible 2D-MHD with Power Law-Type Nonlinear Viscous Fluid by Jae-Myoung Kim

“…In this paper, we establish the global existence and uniqueness of a weak solution u,b depending on a number q in ℝ2. Moreover, the energy norm of the weak solutions to the fluid flows has decay rate 1+t−1/2.…”
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