相关论文: Dependence Result of the Weak Solution of Robin Bo…
By applying Mountain Pass Lemma, Ekeland's and Ricceri's variational principle, Fountain Theorem, we prove the existence and multiplicity of solutions for the following Robin problem \begin{equation*} \left\{ \begin{array}{cc}…
In this paper we study the following boundary value problem involving the weak p-Laplacian. \begin{equation*} \quad -M(\|u\|_{\mathcal{E}_p}^p)\Delta_p u = h(x,u) \; \text{in}\; \mathcal{S}\setminus\mathcal{S}_0; \quad u = 0 \; \mbox{on}\;…
We prove the existence of a principal eigenvalue associated to the $\infty$-Laplacian plus lower order terms and the Neumann boundary condition in a bounded smooth domain. As an application we get uniqueness and existence results for the…
Let $\Omega \subset \mathbb R^N$, $N \geq 2$, be a smooth bounded domain. We consider a boundary value problem of the form $$-\Delta u = c_{\lambda}(x) u + \mu(x) |\nabla u|^2 + h(x), \quad u \in H^1_0(\Omega)\cap L^{\infty}(\Omega)$$ where…
We obtain estimates on the continuous dependence on the coefficient for second order non-linear degenerate Neumann type boundary value problems. Our results extend previous work of Cockburn et.al., Jakobsen-Karlsen, and Gripenberg to…
In this work, we study the existence and multiplicity of solutions for the following problem \begin{equation}\label{probaa1} \left\{ \begin{aligned} -(\Delta)_{p}^{s} u + V(x)|u|^{p-2}u &= \lambda f(u),&x\in\Omega; u&=0,&x\in…
The purpose of this paper is to investigate the existence of three different weak solutions to a nonlinear elliptic problem that is governed by the weighted {\varphi}-Laplacian operator and subjected to Dirichlet boundary conditions. We…
Any positive power of the Laplacian is related via its Fourier symbol to a hypersingular integral with finite differences. We show how this yields a pointwise evaluation which is more flexible than other notions used so far in the…
By means of a suitable weighted rearrangement, we obtain various apriori bounds for the solutions to a Robin problem. Among other things, we derive a family of Faber-Krahn type inequalities.
We consider a Laplacian on the one-sided full shift space over a finite symbol set, which is constructed as a renormalized limit of finite difference operators. We propose a weak definition of this Laplacian, analogous to the one in…
The main goal of this paper is the study of two kinds of nonlinear problems depending on parameters in unbounded domains. Using a nonstandard variational approach, we first prove the existence of bounded solutions for nonlinear eigenvalue…
The paper provides new upper and lower bounds for the multivariate Laplace approximation under weak local assumptions. Their range of validity is also given. An application to an integral arising in the extension of the Dixon's identity is…
In this paper, we investigate the existence and uniqueness of solutions for the following model problem, involving singularities and inhomogeneous Robin boundary conditions \begin{equation*} \left\{ \begin{array}{ll}…
In this paper, we consider Dirichlet boundary value problem involving the anisotropic $p(x)$-Laplacian, where $p(x)= (p_1(x), ..., p_n(x))$, with $p_i(x)> 1$ in $\overline{\Omega}$. Using the topological degree constructed by Berkovits, we…
We consider a nonlinear Robin problem driven by the $p$-Laplacian plus an indefinite potential. The reaction term is of arbitrary growth and only conditions near zero are imposed. Using critical point theory together with suitable…
In this paper, we want to study the asymptotic behavior of the first $p$-Laplacian eigenvalue, with Robin boundary conditions, with negative boundary parameter. In particular, we prove that the limit of the eigenfunctions is a viscosity…
In this paper we study a system of boundary value problems involving weak p-Laplacian on the Sierpi\'nski gasket in $\mathbb{R}^2$. Parameters $\lambda, \gamma, \alpha, \beta$ are real and $1<q<p<\alpha+\beta.$ Functions $a,b,h :…
We study the asymptotic behaviour, as $p\to 1^{+}$, of the solutions of the following inhomogeneous Robin boundary value problem: \begin{equation} \label{pbabstract} \tag{P} \left\{\begin{array}{ll} \displaystyle -\Delta_p u_p = f &…
We consider a number of boundary value problems involving the $p$-Laplacian. The model case is $-\Delta_p u=V|u|^{p-2}u$ for $u\in W_0^{1,2}(D)$ with $D$ a bounded domain in ${\bf R}^n$. We derive necessary conditions for the existence of…
The global-in-time existence of bounded weak solutions to general cross-diffusion systems describing the evolution of $n$ population species is proved. The equations are considered in a bounded domain with no-flux boundary conditions. The…