For a general class of autonomous quasi-linear elliptic equations on R^n we prove the existence of a least energy solution and show that all least energy solutions do not change sign and are radially symmetric up to a translation in R^n.
We study the existence and multiplicity of nonnegative solutions, as well as the behaviour of corresponding parameter-dependent branches, to the equation $-Delta u = (1-u) u^m - lambda u^n$ in a bounded domain $Omega subset mathbb{R}^N$ endowed with
the zero Dirichlet boundary data, where $0<m leq 1$ and $n>0$. When $lambda > 0$, the obtained solutions can be seen as steady states of the corresponding reaction-diffusion equation describing a model of isothermal autocatalytic chemical reaction with termination. In addition to the main new results, we formulate a few relevant conjectures.
We prove the existence of positive solutions to a sys- tem of k non-linear elliptic equations corresponding to standing- wave k-uples solutions to a system of non-linear Klein-Gordon equations. Our solutions are characterised by a small energy/charge ratio, appropriately defined.
For a class of singular divergence type quasi-linear parabolic equations with a Radon measure on the right hand side we derive pointwise estimates for solutions via the nonlinear Wolff potentials.
We study boundary blow-up solutions of semilinear elliptic equations $Lu=u_+^p$ with $p>1$, or $Lu=e^{au}$ with $a>0$, where $L$ is a second order elliptic operator with measurable coefficients. Several uniqueness theorems and an existence theorem are obtained.
In this paper, we show $C^{2,alpha}$ interior estimates for viscosity solutions of fully non-linear, uniformly elliptic equations, which are close to linear equations and we also compute an explicit bound for the closeness.
Louis Jeanjean
,Marco Squassina
.
(2008)
.
"Existence and symmetry of least energy solutions for a class of quasi-linear elliptic equations"
.
Marco Squassina
هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا