Nonlinear Differential Equations and Applications NoDEA
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Solutions of a quasilinear Schrödinger–Poisson system with linearly bounded nonlinearities
Nonlinear Differential Equations and Applications NoDEA - - 2024
Convergence of approximate solutions to an elliptic–parabolic equation without the structure condition
Nonlinear Differential Equations and Applications NoDEA - Tập 19 - Trang 695-717 - 2011
We study the Cauchy–Dirichlet problem for the elliptic–parabolic equation
$$b(u)_t + {\rm div} F(u) - \Delta u = f$$
in a bounded domain. We do not assume the structure condition
$$b(z) = b(\hat z) \Rightarrow F(z) = F(\hat z).$......
Wellposedness in the Lipschitz class for a quasi-linear hyperbolic system arising from a model of the atmosphere including water phase transitions
Nonlinear Differential Equations and Applications NoDEA - Tập 21 Số 2 - Trang 263-287 - 2014
In this paper wellposedness is proved for a diagonal quasilinear hyperbolic system containing integral quadratic and Lipschitz continuous terms which prevent from looking for classical solutions in Sobolev spaces. It is the hyperbolic part of the system introduced in [Selvaduray and Fujita Yashima on Atti dell’Accademia delle Scienze di Torino 2011] as a model for air motion in $${\mathbf{R}^3}$$ ......
Multiple solutions of a sublinear Schrödinger equation
Nonlinear Differential Equations and Applications NoDEA - - 2007
Nonlinear diffusion equations driven by the p(·)-Laplacian
Nonlinear Differential Equations and Applications NoDEA - Tập 20 - Trang 37-64 - 2012
This paper is concerned with nonlinear diffusion equations driven by the p(·)-Laplacian with variable exponents in space. The well-posedness is first checked for measurable exponents by setting up a subdifferential approach. The main purposes are to investigate the large-time behavior of solutions as well as to reveal the limiting behavior of solutions as p(·) diverges to the infinity in the whole......
Three-term spectral asymptotics for nonlinear Sturm-Liouville problems
Nonlinear Differential Equations and Applications NoDEA - Tập 9 - Trang 239-254 - 2002
We consider the nonlinear Sturm-Liouville problem¶¶
$ -u''(t) + \vert u(t)\vert^{p-1}u(t) + f(u(t)) = \lambda u(t),\\ \enskip t \in I := (0, 1), \enskip u(0) = u(1) = 0, $
¶¶ where
$ p > 1 $
is a constant and
$ \lambda > 0 $
is an eigenvalue parameter. We establish the three-term asympto......
Semi-linear fractional $$\varvec{\sigma }$$ -evolution equations with mass or power non-linearity
Nonlinear Differential Equations and Applications NoDEA - Tập 25 - Trang 1-43 - 2018
In this paper we study the global (in time) existence of small data solutions to semi-linear fractional
$$\sigma $$
-evolution equations with mass or power non-linearity. Our main goal is to explain on the one hand the influence of the mass term and on the ot......
Global bifurcation and multiplicity results for Sturm-Liouville problems
Nonlinear Differential Equations and Applications NoDEA - Tập 14 - Trang 559-568 - 2007
We prove the multiplicity theorem for the problem
$$\left\{\begin{array}{l} {u''(t) + \mu u(t) + \varphi (t,u(t),u'(t)) = 0\quad \hbox{for a. e.}\, t \in (a,b)}\\ {l(u) = 0,}\end{array}\right.$$
with Sturm-Liouville boundary conditions l, and function φ satisfying Caratheodory conditions. We assume tha......
Differential equations with bounded positive Green’s functions and generalized Aizerman’s hypothesis
Nonlinear Differential Equations and Applications NoDEA - Tập 11 - Trang 137-150 - 2004
We derive conditions for the positivity
and boundedness of the Green functions of the higher order linear nonautonomous ODE.
By virtue of these conditions, the existence of positive solutions
for a class of nonlinear equations is proved. In addition,
upper and lower estimates for the Green functions
are established. Moreover, it is shown that nonlinear equations, having separated nonaut......
Stochastic Lyapunov method
Nonlinear Differential Equations and Applications NoDEA - Tập 2 - Trang 511-525 - 1995
This paper is devoted to stability properties of solutions to stochastic differential equations obtained by a stochastic Lyapunov method.
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