Existence and Uniqueness of Weak Solutions for a New Class of Convex Optimization Problems Related to Image Analysis by Anas Tiarimti Alaoui, Mostafa Jourhmane

“…After that, the existence and uniqueness of weak solutions for the corresponding Euler–Lagrange equation are proven in an appropriate functional space, and a consistent and stable numerical model is also shown. …”
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A New Proof of Existence of Positive Weak Solutions for Sublinear Kirchhoff Elliptic Systems with Multiple Parameters by Salah Mahmoud Boulaaras, Rafik Guefaifia, Bahri Cherif, Sultan Alodhaibi

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On the Differentiability of Weak Solutions of an Abstract Evolution Equation with a Scalar Type Spectral Operator on the Real Axis by Marat V. Markin

“…Also, proved is the following inherent smoothness improvement effect explaining why the case of the strong finite differentiability of the weak solutions is superfluous: if every weak solution of the equation is strongly differentiable at 0, then all of them are strongly infinite differentiable on R.…”
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Existence of a weak solution to a regularized moving boundary fluid-structure interaction problem with poroelastic media by Kuan, Jeffrey, Čanić, Sunčica, Muha, Boris

“…Namely, in [1] we will show that, in the case of a Biot poroviscoelastic matrix, the moving boundary problem obtained in the singular limit as the thickness of the plate tends to zero, has a weak solution.…”
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On Existence of Multiplicity of Weak Solutions for a New Class of Nonlinear Fractional Boundary Value Systems via Variational Approach by Fares Kamache, Salah Mahmoud Boulaaras, Rafik Guefaifia, Nguyen Thanh Chung, Bahri Belkacem Cherif, Mohamed Abdalla

“…More precisely, we establish the existence of at least three weak solutions for the problem using variational methods combined with the critical point theorem due to Bonano and Marano. …”
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Existence of Positive Weak Solutions for a New Class of p,q Laplacian Nonlinear Elliptic System with Sign-Changing Weights by Rafik Guefaifia, Salah Mahmoud Boulaaras, Sultan Alodhaibi, Salem Alkhalaf

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Multiplicity Results of Solutions to the Fractional <i>p</i>-Laplacian Problems of the Kirchhoff–Schrödinger–Hardy Type by Yun-Ho Kim

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Nonstationary Heat Equation with Nonlinear Side Condition by Tomas Belickas, Kristina Kaulakytė, Gintaras Puriuškis

Subjects: “…nonstationary heat equation, inverse problem, very weak solution, nonlinear side condition…”
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Existence and blow up for viscoelastic hyperbolic equations with variable exponents by Ying Chu, Bo Wen, Libo Cheng

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Weak solutions for a class of quasilinear elliptic equation containing the $p(\cdot )$-Laplacian and the mean curvature operator in a variable exponent Sobolev space by Junichi Aramaki

“…We show the existence of one, two and infinitely many nontrivial weak solutions of the equation according to the conditions on given functions.…”
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Boundary value problems for partial differential equations with piecewise contant delay by Joseph Wiener

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The topological degree method for equations of the Navier-Stokes type by V. T. Dmitrienko, V. G. Zvyagin

Subjects: “…Weak solutions…”
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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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