Related papers: On singular $p$-Laplacian problems with discontinu…
We provide a new result on the existence of extremal solutions for second-order Dirichlet problems with deviation argument. As a novelty in this work, the nonlinearity need not be continuous or monotone. In order to obtain this new result,…
We extend to the case of a system involving p-Laplacians, the monotonicity and symmetry results of Damascelli and Pacella obtained in the case of a scalar p-Laplace equation with $1<p<2$. For this purpose, we use the moving hyperplanes…
An old problem since Leray \cite{Le:1} asks whether homogeneous D solutions of the 3 dimensional Navier-Stokes equation in $\mathbb{R}^3$ or some noncompact domains are 0. In this paper, we give a positive solution to the problem in two…
We present a result of existence of infinitely many solutions for the Dirichlet problem involving the p-Laplacian in annular domains, when $p\leq N$, contouring the failure of compactness of $W^{1,p}(\Omega)$ in $C^0(\bar{\Omega})$ applying…
We prove existence, multiplicity, and bifurcation results for $p$-Laplacian problems involving critical Hardy-Sobolev exponents. Our results are mainly for the case $\lambda \ge \lambda_1$ and extend results in the literature for $0 <…
A Dirichlet problem driven by the $(p,q)$-Laplace operator and an asymmetric concave reaction with positive parameter is investigated. Four nontrivial smooth solutions (two positive, one negative, and the remaining nodal) are obtained once…
The inhomogeneous incompressible Navier-Stokes equations with fractional Laplacian dissipations in the multi-dimensional whole space are considered. The existence and uniqueness of global strong solution with vacuum are established for…
We establish existence results for a class of mixed anisotropic and nonlocal $p$-Laplace equation with singular nonlinearities. We consider both constant and variable singular exponents. Our argument is based on an approximation method. To…
In this paper we study weighted singular $p$-Laplace equations involving a bounded weight function which can be discontinuous. Due to its discontinuity classical regularity results cannot be applied. Based on Nehari manifolds we prove the…
In this paper, we use bifurcation method to investigate the existence and multiplicity of one-sign solutions of the $p$-Laplacian involving a linear/superlinear nonlinearity with zeros. To do this, we first establish a bifurcation theorem…
We study an elliptic equation, with homogeneous Dirichlet boundary conditions, driven by a mixed type operator (the sum of the Laplacian and the fractional Laplacian), involving a parametric reaction and an undetermined source term.…
We consider nonlinear elliptic problems involving a nonlocal operator: the square root of the Laplacian in a bounded domain with zero Dirichlet boundary conditions. For positive solutions to problems with power nonlinearities, we establish…
We investigate the multiplicity and uniqueness of positive solutions for the superlinear singular $(p,q)$-Laplacian equation \begin{eqnarray*} \begin{cases} -\Delta_p u-\Delta_q u+a(x)u^{p-1}+b(x)u^{q-1}=f(x)u^{-\gamma}+\lambda…
We make use of the Guo-Krasnoselskii fixed point theorem on cones to prove existence of positive solutions to a non local p-Laplacian boundary value problem on time scales arising in many applications.
We establish existence and uniqueness of solution for the homogeneous Dirichlet problem associated to a fairly general class of elliptic equations modeled by $$ -\Delta u= h(u){f} \ \ \text{in}\,\ \Omega, $$ where $f$ is an irregular datum,…
We provide symmetrization results in the form of mass concentration comparisons for fractional singular elliptic equations in bounded domains, coupled with homogeneous external Dirichlet conditions. Two types of comparison results are…
In this article, we focus on a doubly nonlinear nonlocal parabolic initial boundary value problem driven by the fractional $p$-Laplacian equipped with homogeneous Dirichlet boundary conditions on a domain in $\mathbb{R}^{d}$ and composed…
We provide a unified strategy to show that solutions of dynamic programming principles associated to the $p$-Laplacian converge to the solution of the corresponding Dirichlet problem. Our approach includes all previously known cases for…
We prove that solutions to Cauchy problems related to the $p$-parabolic equations are stable with respect to the nonlinearity exponent $p$. More specifically, solutions with a fixed initial trace converge in an $L^q$-space to a solution of…
In this paper we study a double-phase problem involving the 1-Laplacian with non-homogeneous Dirichlet boundary conditions and show the existence and uniqueness of a solution in a suitable weak sense. We also provide a variational…