Results 1 to 10 of about 189,248 (240)
A class of fourth-order parabolic equation with logarithmic nonlinearity [PDF]
Journal of Inequalities and Applications, 2018 In this paper, we study a class of fourth-order parabolic equation with the logarithmic nonlinearity. By using the potential well method, we obtain the existence of the unique global weak solution. In addition, we also obtain results of decay and blow-up
Pingping Li, Changchun Liu
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Fractional p(·)-Kirchhoff Type Problems Involving Variable Exponent Logarithmic Nonlinearity
Fractal and Fractional, 2022 In this paper, we investigate a fractional p(·)-Kirchhoff type problem involving variable exponent logarithmic nonlinearity. With the help of the Nehari manifold approach, the existence and multiplicity of nontrivial weak solutions for the above problem ...
Jiabin Zuo +2 more
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On a viscoelastic heat equation with logarithmic nonlinearity [PDF]
Electronic Journal of Qualitative Theory of Differential Equations, 2022 This work deals with the following viscoelastic heat equations with logarithmic nonlinearity \begin{align*} u_t-\Delta u+\int_{0}^{t}g(t-s)\Delta u(s)ds=\vert u\vert^{p-2}u\ln\vert u\vert.
Nguyen Van Y, Nhan Le, Le Xuan Truong
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Journal of Mathematics, 2023 In this paper, a new pseudoparabolic equation with logarithmic nonlinearity of variable exponents is investigated. By using the energy functional and the classical potential well, we obtain the global existence and blow-up results of weak solutions with ...
Rongting Pan, Yunzhu Gao, Qiu Meng
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Ground states for fractional nonlocal equations with logarithmic nonlinearity [PDF]
Opuscula Mathematica, 2022 In this paper, we study on the fractional nonlocal equation with the logarithmic nonlinearity formed by \[\begin{cases}\mathcal{L}_{K}u(x)+u\log|u|+|u|^{q-2}u=0, & x\in\Omega,\\ u=0, & x\in\mathbb{R}^{n}\setminus\Omega,\end{cases}\] where \(2\lt ...
Lifeng Guo, Yan Sun, Guannan Shi
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Boundary Value Problems, 2022 In this article, we consider a viscoelastic plate equation with past history, nonlinear damping, and logarithmic nonlinearity. We prove explicit and general decay rate results of the solution to the viscoelastic plate equation with past history.
Bhargav Kumar Kakumani +1 more
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Logarithmic estimates for mean-field models in dimension two and the Schrödinger–Poisson system
Comptes Rendus. Mathématique, 2022 In dimension two, we investigate a free energy and the ground state energy of the Schrödinger–Poisson system coupled with a logarithmic nonlinearity in terms of underlying functional inequalities which take into account the scaling invariances of the ...
Dolbeault, Jean +2 more
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Oscillatory bifurcation problems for ODEs with logarithmic nonlinearity
Open Mathematics, 2021 We study the global structure of the oscillatory perturbed bifurcation problem which comes from the stationary logarithmic Schrödinger equation −u″(t)=λ(log(1+u(t))+sinu(t)),u(t)>0,t∈I≔(−1,1),u(±1)=0,-{u}^{^{\prime\prime} }\left(t)=\lambda (\log \left(1 ...
Shibata Tetsutaro
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Partial Differential Equations in Applied Mathematics, 2021 This paper is concerned with the existence and exponential stability of the global solution to a Klein–Gordon equation of Kirchhoff-Carrier type with strong damping −Δutand logarithmic source term uln|u|R2.
S.M.S. Cordeiro +3 more
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Global existence and blow up of solution for semi-linear hyperbolic equation with the product of logarithmic and power-type nonlinearity [PDF]
Opuscula Mathematica, 2020 In this paper we consider the semilinear wave equation with the multiplication of logarithmic and polynomial nonlinearities. We establish the global existence and finite time blow up of solutions at three different energy levels (\(E(0)\lt d\), \(E(0)=d\)
Wei Lian, Md Salik Ahmed, Runzhang Xu
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