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Using a multiple critical points theorem for locally Lipschitz continuous functionals, we establish the existence of at least three distinct solutions for a parametric discrete differential inclusion problem involving a real symmetric and…

In this paper, we derive a new $p$-Logarithmic Sobolev inequality and optimal continuous and compact embeddings into Orlicz-type spaces of the function space associated with the logarithmic $p$-Laplacian. As an application of these results,…

We study a nonlinear, nonlocal Dirichlet problem driven by the fractional p-Laplacian, involving a (p-1)-sublinear reaction. By means of a weak comparison principle we prove uniqueness of the solution. Also, comparing the problem to…

We study the existence of nontrivial solutions for a nonlinear fractional elliptic equation in presence of logarithmic and critical exponential nonlinearities. This problem extends [5] to fractional $N/s$-Laplacian equations with…

Let $p,q$ be functions on $\mathbb{R}^{N}$ satisfying $1\ll q\ll p\ll N$, we consider $p(x)$-Laplacian problems of the form \[ \left\{ \begin{array} [c]{l}% -\Delta_{p(x)}u+V(x)\vert u\vert ^{p(x)-2}u=\lambda\vert u\vert…

This paper mainly investigates the analytic solutions for the approximation of $p$-Laplacian problem. Through an approximation mechanism, we convert the nonlinear partial differential equation with Dirichlet boundary into a sequence of…

In this paper, we prove the existence of a unique positive entropy solution to a fractional Laplacian problem involving nonlinear singular terms and also a non-negative bounded Radon measure as a source term.

We consider a nonlinear Neumann problem driven by a $p$-Laplacian-type, nonhomogeneous elliptic differential operator and a Carath\'eodory reaction term. In this paper we prove the existence of two extremal constant sign smooth solutions…

We consider a nonlinear Dirichlet problem driven by the $(p,q)$-Laplacian with $1<q<p$. The reaction is parametric and exhibits the competing effects of a singular term and of concave and convex nonlinearities. We are looking for positive…

We prove a bifurcation and multiplicity result that is independent of the dimension N for a critical p-Laplacian problem that is the analog of the Brezis-Nirenberg problem for the quasilinear case. This extends a result in the literature…

We look for nonconstant, positive, radially nondecreasing solutions of the quasilinear equation $-\Delta_p u+u^{p-1}=f(u)$ with $p>2$, in the unit ball $B$ of $\mathbb R^N$, subject to homogeneous Neumann boundary conditions. The…

In this paper, we provide a direct approach to the existence and uniqueness of strong (in the probabilistic sense) and weak (in the PDE sense) solutions to quasilinear stochastic partial differential equations, which are neither monotone…

We consider the natural time-dependent fractional $p$-Laplacian equation posed in the whole Euclidean space, with parameter $1<p<2$ and fractional exponent $s\in (0,1)$. Rather standard theory shows that the Cauchy Problem for data in the…

This work deals with the existence of at least two positive solutions for the class of quasilinear elliptic equations with cylindrical singularities and multiple critical nonlinearities that can be written in the form \begin{align*}…

By using the fibering method jointly with Nehari manifold techniques, we obtain the existence of multiple solutions to a fractional $p$-Laplacian system involving critical concave-convex nonlinearities provided that a suitable smallness…

We study the weakly coupled critical elliptic system \begin{equation*} \begin{cases} -\Delta u=\mu_{1}|u|^{2^{*}-2}u+\lambda\alpha |u|^{\alpha-2}|v|^{\beta}u & \text{in }\Omega,\\ -\Delta v=\mu_{2}|v|^{2^{*}-2}v+\lambda\beta…

It is considered a semilinear elliptic partial differential equation in $\mathbb{R}^N$ with a potential that may vanish at infinity and a nonlinear term with subcritical growth. A positive solution is proved to exist depending on the…

The paper considers the Schrodinger-Maxwell system with supercritical nonlinearitie. We prove the existence of at least one non-trivial weak solution. This result is already known for the subcritical case. In this paper, we extend it to the…

The existence of a nontrivial solution is proved for a class of quasilinear elliptic equations involving, as principal part, either the p-Laplace operator or the operator related to the p-area functional, and a nonlinearity with p-linear…

In this paper we establish existence, nonexitence and regularity of positive solutions for a class of singular quasilinear elliptic systems subject to (super-) homogeneous condition. The approach is based on sub-supersolution methods for…