Results 61 to 70 of about 93,033 (295)
Multiple Nontrivial Solutions of Semilinear Elliptic Equations [PDF]
Proceedings of the American Mathematical Society, 1988 We give a condition for a semilinear elliptic equation to have two nontrivial solutions. Our condition does not demand any differentiability of the nonlinear term.
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Mathematical Methods in the Applied Sciences, Volume 48, Issue 16, Page 14890-14908, 15 November 2025.ABSTRACT We analyze nonlinear degenerate coupled partial differential equation (PDE)‐PDE and PDE‐ordinary differential equation (ODE) systems that arise, for example, in the modelling of biofilm growth. One of the equations, describing the evolution of a biomass density, exhibits degenerate and singular diffusion.
K. Mitra, S. Sonner
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Multiple solutions of nonlinear partial functional differential equations and systems
Electronic Journal of Qualitative Theory of Differential Equations, 2019 We shall consider weak solutions of initial-boundary value problems for semilinear and nonlinear parabolic differential equations with certain nonlocal terms, further, systems of elliptic functional differential equations.
László Simon
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On semilinear elliptic equations with diffuse measures [PDF]
Nonlinear Differential Equations and Applications NoDEA, 2018 We consider semilinear equation of the form $$-Lu=f(x,u)+\mu $$-Lu=f(x,u)+μ, where L is the operator corresponding to a transient symmetric regular Dirichlet form $${\mathcal {E}}$$E, $$\mu $$μ is a diffuse measure with respect to the capacity associated
Tomasz Klimsiak, A. Rozkosz
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Semilinear elliptic equations on rough domains
Journal of Differential Equations, 2023 39 ...
Wolfgang Arendt, Daniel Daners
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Existence of Weak Solutions for a Degenerate Goursat‐Type Linear Problem
Mathematical Methods in the Applied Sciences, Volume 48, Issue 15, Page 14334-14341, October 2025.ABSTRACT For a generalization of the Gellerstedt operator with mixed‐type Dirichlet boundary conditions to a suitable Tricomi domain, we prove the existence and uniqueness of weak solutions of the linear problem and for a generalization of this problem.
Olimpio Hiroshi Miyagaki +2 more
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Construction of blow‐up solutions for Liouville systems
Proceedings of the London Mathematical Society, Volume 131, Issue 4, October 2025.Abstract We study the following Liouville system defined on a flat torus −Δui=∑j=1naijρjhjeuj∫Ωhjeuj−1,uj∈Hper1(Ω)fori∈I={1,…,n},$$\begin{equation*} {\left\lbrace \def\eqcellsep{&}\begin{array}{lr}-\Delta u_i=\sum _{j=1}^n a_{ij}\rho _j{\left(\frac{h_j e^{u_j}}{\int _\Omega h_j e^{u_j}}-1\right)},\\[3pt] u_j\in H_{per}^1(\Omega)\mbox{ for }i\in I ...
Zetao Cheng, Haoyu Li, Lei Zhang
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Locating the peaks of semilinear elliptic systems
, 2005 We consider a system of weakly coupled singularly perturbed semilinear elliptic equations. First, we obtain a Lipschitz regularity result for the associated ground energy function $\Sigma$ as well as representation formulas for the left and the right ...
Pomponio, Alessio, Squassina, Marco
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Parallelization of Faber Polynomial Based Propagators for Laser Applications
International Journal of Numerical Modelling: Electronic Networks, Devices and Fields, Volume 38, Issue 4, July/August 2025.ABSTRACT In order to simulate a laser system, the evaluation of a complex semilinear master equation is needed, including the description of the wave propagation by Maxwell's equations and appropriate rate equations. The denser the spatial discretization, the slower the computation time of the time‐dependent propagator.
Wladimir Plotnikov, Dirk Schulz
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Electronic Journal of Differential Equations, 2000 solutions to nonlinear equations and to (non)resonant semilinear equations involving nonlinear perturbations of Fredholm maps of index zero. We apply our results to semilinear elliptic, and to semilinear parabolic and hyperbolic periodic boundary-value ...
P. S. Milojevic
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