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Existence of nontrivial weak solutions for a quasilinear Choquard equation [PDF]
Journal of Inequalities and Applications, 2018 We are concerned with the following quasilinear Choquard equation: −Δpu+V(x)|u|p−2u=λ(Iα∗F(u))f(u)in RN,F(t)=∫0tf(s)ds, $$ -\Delta_{p} u+V(x)|u|^{p-2}u=\lambda\bigl(I_{\alpha} \ast F(u)\bigr)f(u) \quad \text{in } \mathbb {R}^{N}, \qquad F(t)= \int_{0}^{t}
Jongrak Lee +3 more
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Dimensionalities of Weak Solutions in Hydrogenic Systems [PDF]
Journal of Physics A: Mathematical and General, 2006 A close inspection on the 3D hydrogen atom Hamiltonian revealed formal eigenvectors often discarded in the literature. Although not in its domain, such eigenvectors belong to the Hilbert space, and so their time evolution is well defined.
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Weak solutions of generated Jacobian equations
Mathematics in Engineering, 2023 We prove two groups of relationships for weak solutions to generated Jacobian equations under proper assumptions on the generating functions and the domains, which are generalizations for the optimal transportation case and the standard Monge-Ampère case
Feida Jiang
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On the solvability of Dirichlet problem for the weighted p-Laplacian [PDF]
Opuscula Mathematica, 2012 The paper investigates the existence and uniqueness of weak solutions for a non-linear boundary value problem involving the weighted \(p\)-Laplacian. Our approach is based on variational principles and representation properties of the associated spaces.
Ewa Szlachtowska
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A variational approach for mixed elliptic problems involving the p-Laplacian with two parameters
Boundary Value Problems, 2022 By exploiting an abstract critical-point result for differentiable and parametric functionals, we show the existence of infinitely many weak solutions for nonlinear elliptic equations with nonhomogeneous boundary conditions. More accurately, we determine
Armin Hadjian, Juan J. Nieto
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Global weak solutions of nonlinear rotation-Camassa-Holm model
AIMS Mathematics, 2023 A nonlinear rotation-Camassa-Holm equation, physically depicting the motion of equatorial water waves and having the Coriolis effect, is investigated. Using the viscous approximation tool, we obtain an upper bound estimate about the space derivative of ...
Zheng Dou, Kexin Luo
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Harmonic solutions and weak solutions of two-dimensional rotational incompressible Euler equations
Partial Differential Equations in Applied Mathematics, 2022 In this paper, two families of exact solutions to two-dimensional incompressible rotational Euler equations are constructed by connecting the Euler equations with the Laplace equation via a stream function.
Yang Chen, Yunhu Wang, Manwai Yuen
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Local Hölder Regularity of Weak Solutions for Singular Parabolic Systems of p-Laplacian Type
Cauchy: Jurnal Matematika Murni dan Aplikasi, 2021 In this paper, the Hölder regularity of weak solutions for singular parabolic systems of p-Laplacian type is investigated. By the Poincare inequality, we show that its weak solutions within Hölder space.
Khoirunisa Khoirunisa +2 more
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Relaxation and weak solutions of nonlocal semilinear evolution systems
Advances in Difference Equations, 2019 We give a relatively short proof of the fact that the solution set of a nonlocal semilinear differential inclusion is dense in the weak solution set of the corresponding convexified system.
N. Javaid +3 more
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Weak solutions to Allen-Cahn-like equations modelling consolidation of porous media [PDF]
, 2016 We study the weak solvability of a system of coupled Allen--Cahn--like equations resembling cross--diffusion which is arising as a model for the consolidation of saturated porous media.
Cirillo, Emilio Nicola Maria +2 more
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