Results 21 to 30 of about 190 (133)
Multiple solutions for fourth order elliptic problems with p(x)-biharmonic operators
, 2016 We study the multiplicity of weak solutions to the following fourth order nonlinear elliptic problem with a \(p(x)\)-biharmonic operator \[\begin{cases}\Delta^2_{p(x)}u+a(x)|u|^{p(x)-2}u=\lambda f(x,u)\quad\text{ in }\Omega,\\ u=\Delta u=0\quad\text{ on }
Kong, L., Lingju Kong
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Ground state solutions for p-biharmonic equations
, 2017 In this article we study the p-biharmonic equation $$ \Delta_p^2u+V(x)|u|^{p-2}u=f(x,u),\quad x\in\mathbb{R}^N, $$ where $\Delta_p^2u=\Delta(|\Delta u|^{p-2}\Delta u)$ is the p-biharmonic operator.
Haibo Chen +2 more
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On a p(x) $p(x)$-biharmonic problem with Navier boundary condition
, 2018 In this paper, we study a p(x) $p(x)$-biharmonic equation with Navier boundary condition {Δp(x)2u+a(x)|u|p(x)−2u=λf(x,u)+μg(x,u)in Ω,u=Δu=0on ∂Ω. $$ \textstyle\begin{cases} \Delta^{2}_{p(x)}u+a(x)|u|^{p(x)-2}u= \lambda f(x,u)+\mu g(x,u)\quad \text{in ...
Zheng Zhou
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, 2017 The aim of this paper is to establish the existence and multiplicity of solutions for a class of nonlocal problem involving the p(x)-biharmonic operator.
Omar Darhouche
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Thermal Damage to the Skin From 5.6 GHz Microwave Exposures in Swine
Bioelectromagnetics, Volume 47, Issue 4, May 2026.ABSTRACT A study of burn thresholds from superficially penetrating radio‐frequency (RF) energy at 5.6 GHz for swine skin was conducted. The study estimated the thresholds for superficial, partial‐thickness, and full‐thickness burn severities after 20 s of exposure at power densities of 4–8 W/cm2. Biopsies were collected from each burn site at 1, 24, 72,
James E. Parker +7 more
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DJ4Earth: Differentiable, and Performance‐Portable Earth System Modeling via Program Transformations
Journal of Advances in Modeling Earth Systems, Volume 18, Issue 5, May 2026.Abstract Differentiable Earth system models (ESMs) enable powerful applications such as sensitivity analysis, gradient‐based calibration, state estimation, boundary flux inversions, uncertainty quantification, and online machine learning. Reverse‐mode automatic differentiation (AD) efficiently provides gradients for such tasks, yet models have rarely ...
William S. Moses +19 more
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EXISTENCE OF ONE WEAK SOLUTION FOR p(x)-BIHARMONIC EQUATIONS INVOLVING A CONCAVE-CONVEX NONLINEARITY
, 2017 In the present paper, using variational approach and the theory of the variable exponent Lebesgue spaces, the existence of nontrivial weak solutions to a fourth order elliptic equation involvinga p(x)-biharmonic operator and a concave-convex nonlinearity
Alisoy, Gulizar +2 more
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Asymmetries in Anticyclone Catalyze Submesoscale Motions
Geophysical Research Letters, Volume 53, Issue 7, 16 April 2026.Abstract Oceanic mesoscale eddies are often asymmetric, exhibiting horizontal deformation and vertical tilt, yet the implications of these structural asymmetries for finer‐scale dynamics remain poorly understood. Based on a series of high‐resolution numerical experiments, we found that asymmetric anticyclones act as potent catalysts for submesoscale ...
Xianliang Wu, Hong Li, Fanghua Xu
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Journal of Geophysical Research: Solid Earth, Volume 131, Issue 4, April 2026.Abstract Volcanic calderas are large depressions formed by the rapid collapse of overlying rock into a magma chamber during eruptions. We utilize Smoothed Particle Hydrodynamics (SPH), a continuum, meshfree numerical method, to study the 2018 caldera collapse at Kīlauea volcano in Hawaii.
Enrique M. del Castillo, Paul Segall
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On a Class of PDE Involving
, 2011 The existence of solution for a fourth-order nonlinear partial differential equation (PDE) class involving p-biharmonic operator Δ(|Δu|p−2Δu)=λρ(x)|u|q−2u in Ω, u=Δu=0, on ∂Ω, is proved by applying mountain pass theorem and a local minimization.
Abdelouahed El Khalil
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