Results 31 to 40 of about 1,586 (206)
Nonlinear Periodic Systems with the p-Laplacian: Existence and Multiplicity Results
Abstract and Applied Analysis, 2007 We study second-order nonlinear periodic systems driven by the vector p-Laplacian with a nonsmooth, locally Lipschitz potential function. Under minimal and natural hypotheses on the potential and using variational methods based on the nonsmooth critical ...
Francesca Papalini
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Front Propagation Through a Perforated Wall
Communications on Pure and Applied Mathematics, EarlyView.ABSTRACT We consider a bistable reaction– diffusion equation ut=Δu+f(u)$u_t=\Delta u +f(u)$ on RN${\mathbb {R}}^N$ in the presence of an obstacle K$K$, which is a wall of infinite span with many holes. More precisely, K$K$ is a closed subset of RN${\mathbb {R}}^N$ with smooth boundary such that its projection onto the x1$x_1$‐axis is bounded and that ...
Henri Berestycki +2 more
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The SIR Model in a Moving Population: Propagation of Infection and Herd Immunity
Communications on Pure and Applied Mathematics, EarlyView.ABSTRACT In a collection of particles performing independent random walks on Zd$\mathbb {Z}^d$ we study the spread of an infection with SIR dynamics. Susceptible particles become infected when they meet an infected particle. Infected particles heal and are removed at rate ν$\nu$.
Duncan Dauvergne, Allan Sly
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International Journal of Mathematics and Mathematical Sciences, 1984 In an open bounded region of n-space occupied by a homogeneous and isotropic medium, we control the temperature through the boundary. The normal derivative of the temperature (which measures the appropriate heat flux) is restricted to be nonnegative ...
Ioannis Athanasopoulos
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Homoclinic solutions of singular differential equations with $\phi$-Laplacian
Electronic Journal of Qualitative Theory of Differential Equations, 2018 A singular nonlinear initial value problem (IVP) with a $\phi$-Laplacian of the form $$ (p(t)\phi(u'(t)))'+ p(t)f(\phi(u(t)))=0, \quad u(0)=u_0 \in [L_0,0),\quad u'(0)=0 $$ is investigated on the half-line $[0,\infty)$.
Lukáš Rachůnek, Irena Rachůnková
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Uniqueness for Neumann Problems for Nonlinear Elliptic Equations With Lower Order Terms
Mathematische Nachrichten, EarlyView.ABSTRACT In this paper, we prove uniqueness results for weak solutions to a class of Neumann problems, whose prototype is λ(1+u2)(p−2)/2u−div((1+|∇u|2)(p−2)/2∇u)−div(c(x)(1+|u|2)(τ+1)/2)+b(x)(1+|∇u|2)(σ+1)/2=finΩ(1+|∇u|2)(p−2)/2∇u+c(x)(1+|u|2)(τ+1)/2)·n̲=0on∂Ω,$$\begin{equation*} {\begin{cases} {}\lambda {(1+ u^2)}^{(p-2)/2}u-{\operatorname{div}}({(1+|\
Maria Francesca Betta +3 more
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On Inverse and Implicit Function Theorem for Sobolev Mappings
AxiomsWe extend Clarke’s local inversion theorem for Sobolev mappings. We use this result to find a general implicit function theorem for continuous locally Lipschitz mapping in the first variable and satisfying just a topological condition in the second ...
Mihai Cristea
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Locally Lipschitz Functions and Bornological Derivatives
, 1993 We study the relationships between Gateaux, weak Hadamard and Frechet differentiability and their bornologies for Lipschitz and for convex functions. In particular, Frechet and weak Hadamard differentiabily coincide for all Lipschitz functions if and only if the space is reflexive (an earlier paper of the first two authors shows that these two notions ...
Borwein, Jonathan M. +2 more
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Visibility and Intersection Density for Boolean Models in Hyperbolic Space
Mathematische Nachrichten, EarlyView.ABSTRACT For Poisson particle processes in hyperbolic space we introduce and study concepts analogous to the intersection density and the mean visible volume, which were originally considered in the analysis of Boolean models in Euclidean space. In particular, we determine a necessary and sufficient condition for the finiteness of the mean visible ...
Tillmann Bühler +2 more
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On locally Lipschitz vector-valued invex functions [PDF]
Bulletin of the Australian Mathematical Society, 1993 The four types of invexity for locally Lipschitz vector-valued functions recently introduced by T. W. Reiland are studied in more detail. It is shown that the class of restricted K-invex in the limit functions is too large to obtain desired optimisation theorems and the other three classes are contained in the class of functions which are invex 0 in ...
Yen, N. D., Sach, P. H.
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