Related papers: On some general multiplying solutions results of a…
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 existence and the summability of solutions to a Robin boundary value problem whose prototype is the following: $$ \begin{cases} -\text{div}(b(|u|)\nabla u)=f &\text{in }\Omega,\\[.2cm] \displaystyle\frac{\partial…
In this article, we investigate the existence and multiplicity of solutions to the Robin problem \begin{equation*} \begin{cases} -\Delta u = \lambda f(u) & \text{in } \Omega, \frac{\partial u}{\partial \nu} + \gamma u=0 & \text{on }…
We go further in the investigation of the Robin problem $(P_{\alpha})$: $-\Delta u=a(x)u^{q}$ in $\Omega$, $u\geq0$ in $\Omega$, $\partial_{\nu}u=\alpha u$ on $\partial \Omega$; on a bounded domain $\Omega\subset\mathbb{R}^{N}$, with $a$…
The existence of three smooth solutions, one negative, one positive, and one nodal, to a homogeneous Robin problem with $p$-Laplacian and Carath\'eodory reaction is established. No sub-critical growth condition is taken on. Proofs exploit…
A Robin boundary-value problem with non-homogeneous differential operator, indefinite potential, and reaction defined only near zero is investigated. The existence of one or more nodal solutions is achieved by using truncation,…
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…
We deal with existence and uniqueness of nonnegative solutions to \begin{equation*} \left\{ \begin{array}{l} -\Delta u = f(x) \text{ in }\Omega, \frac{\partial u}{\partial \nu} + \lambda(x) u = \frac{g(x)}{u^\eta} \text{ on }…
We prove an existence result for Robin boundary value problems modeled on \[ \begin{cases} \Delta u + |\nabla u|^2 + \lambda f(x) = 0 & \text{in } \Omega \\ \frac{\partial u}{\partial \nu} + \beta u = 0 & \text{on } \partial\Omega…
We consider semilinear Robin problems driven by the negative Laplacian plus an indefinite potential and with a superlinear reaction term which need not satisfy the Ambrosetti-Rabinowitz condition. We prove existence and multiplicity…
We consider the Robin boundary value problem $\mathrm{div} (A \nabla u) = \mathrm{div} \mathbf{f}+F$ in $\Omega$, $\mathcal{C}^1$ domain, with $(A \nabla u - \mathbf{f})\cdot \mathbf{n} + \alpha u = g$ on $\Gamma$, where the matrix $A$…
In this paper, the existence of smooth positive solutions to a Robin boundary-value problem with non-homogeneous differential operator and reaction given by a nonlinear convection term plus a singular one is established. Proofs chiefly…
In this paper we prove the uniqueness of the critical point for stable solutions of the Robin problem \[ \begin{cases} -\Delta u=f(u)&\text{in }\Omega\\ u>0&\text{in }\Omega\\ \partial_\nu u+\beta u=0&\text{on }\partial\Omega, \end{cases}…
Let $\Omega\subset\mathbb{R}^{N}$ ($N\geq1$) be a smooth bounded domain, $a\in C(\bar{\Omega})$ a sign-changing function, and $0\leq q<1$. We investigate the Robin problem \[ \begin{cases} -\Delta u=a(x)u^{q} & \mbox{in $\Omega$},\\ u\geq0…
In this paper we investigate the existence of multiple solutions for the following two fractional problems \begin{equation*} \left\{\begin{array}{ll} (-\Delta_{\Omega})^{s} u-\lambda u= f(x, u) &\mbox{in} \Omega \\ u=0 &\mbox{in} \partial…
We study a nonlinear Robin problem driven by the $p$-Laplacian and with a reaction term depending on the gradient (the convection term). Using the theory of nonlinear operators of monotone-type and the asymptotic analysis of a suitable…
In this paper we consider an anisotropic Robin problem driven by the $p(x)$-Laplacian and a superlinear reaction. Applying variational tools along with truncation and comparison techniques as well as critical groups, we prove that the…
In \cite{CJ1} M. Jaoua et al. studied the linear approximation of Robin problem on $\Omega$ an open bounded domain of $\R^d$, and they given some important results. In this paper, we study a nonlinear approximation of an elliptic problem…
The existence of two nontrivial smooth solutions to a semilinear Robin problem with indefinite unbounded potential and asymmetric nonlinearity $f$ is established. Both crossing and resonance are allowed. A third nonzero solution exists…
Given $\epsilon \in (0,1)$ and $\lambda > 1$, we address the existence of solutions for the Sinh-Poisson equation with Robin boundary value condition $$ \begin{cases} \Delta u+\epsilon^2 (e^{u} - e^{-u})=0 &\mbox{in }\Omega\\ \frac{\partial…