Browsing by Subject "weak solution"

Now showing 1 - 6 of 6

Access status: Open Access ,
A unique weak solution for a kind of coupled system of fractional Schrödinger equations
(Wydawnictwa AGH, 2020) Abdolrazaghi, Fatemeh; Razani, Abdolrahman
In this paper, we prove the existence of a unique weak solution for a class of fractional systems of Schrödinger equations by using the Minty-Browder theorem in the Cartesian space. To this aim, we need to impose some growth conditions to control the source functions with respect to dependent variables.
Access status: Open Access ,
Eigenvalue problems for anisotropic equations involving a potential on Orlicz-Sobolev type spaces
(2016) Stăncuţ, Ionela-Loredana; Stîrcu, Iulia Dorotheea
In this paper we consider an eigenvalue problem that involves a nonhomogeneous elliptic operator, variable growth conditions and a potential $V$ on a bounded domain in $\mathbb{R}^N$ ($N\geq 3$) with a smooth boundary. We establish three main results with various assumptions. The first one asserts that any $\lambda\gt 0$ is an eigenvalue of our problem. The second theorem states the existence of a constant $\lambda_{*}\gt 0$ such that any $\lambda\in(0,\lambda_{*}]$ is an eigenvalue, while the third theorem claims the existence of a constant $\lambda^{*}\gt 0$ such that every $\lambda\in[\lambda^{*}, \infty)$ is an eigenvalue of the problem.
Access status: Open Access ,
Nonlinear parabolic equation having nonstandard growth condition with respect to the gradient and variable exponent
(Wydawnictwa AGH, 2021) Charkaoui, Abderrahim; Fahim, Houda; Alaa, Nour Eddine
We are concerned with the existence of solutions to a class of quasilinear parabolic equations having critical growth nonlinearity with respect to the gradient and variable exponent. Using Schaeffer's fixed point theorem combined with the sub- and supersolution method, we prove the existence results of a weak solutions to the considered problems.
Access status: Open Access ,
On a class of nonhomogenous quasilinear problems in Orlicz-Sobolev spaces
(2012) Souayah, Asma Karoui
We study the nonlinear boundary value problem $-div ((a_1(|\nabla u(x)|)+a_2(|\nabla u(x)|))\nabla u(x))=\lambda |u|^{q(x)-2}u-\mu |u|^{\alpha(x)-2}u$ in $\Omega$, $u=0$ on $\partial \Omega$, where $\Omega$ is a bounded domain in $\mathbb{R}^N$ with smooth boundary, $\lambda$, $\mu$ are positive real numbers, $q$ and $\alpha$ are continuous functions and $a_1$, $a_2$ are two mappings such that $a_{1}(|t|)t$, $a_{2}(|t|)t$, are increasing homeomorphisms from $\mathbb{R}$ to $\mathbb{R}$. The problem is analysed in the context of Orlicz-Soboev spaces. First we show the existence of infinitely many weak solutions for any $\lambda,\mu \gt 0$. Second we prove that for any $\mu \gt 0$, there exists $\lambda_*$ sufficiently small, and $\lambda^*$ large enough such that for any $\lambda \in (0,\lambda_*)\cup(\lambda^*,\infty)$, the above nonhomogeneous quasilinear problem has a non-trivial weak solution.
Access status: Open Access ,
On the existence of three solutions for quasilinear elliptic problem
(2012) Goncerz, Paweł
We consider a quasilinear elliptic problem of the type $-\Delta_p u = \lambda (f(u)+\mu g(u))$ in $\Omega$, $u|_{\partial \Omega} =0$, where $\Omega \in \mathbb{R}^N$ is an open and bounded set, $f$, $g$ are continuous real functions on $\mathbb{R}$ and $\lambda , \mu \in \mathbb{R}$. We prove the existence of at least three solutions for this problem using the so called three critical points theorem due to Ricceri.
Access status: Open Access ,
Weak solutions for nonlinear fractional differential equations with integral boundary conditions in Banach spaces
(2012) Benchohra, Mouffak; Mostefai, Fatima-Zohra
The aim of this paper is to investigate a class of boundary value problems for fractional differential equations involving nonlinear integral conditions. The main tool used in our considerations is the technique associated with measures of weak noncompactness.