Related papers: Existence of solution to a critical equation with …

In this paper we prove the existence of a weak solution to a doubly nonlinear parabolic fractional $p$-Laplacian equation, which has general doubly non-linearlity including not only the Sobolev subcritical/critical/supercritical cases but…

We discuss the Kirchhoff-type $p$-Laplacian Dirichlet problem containing the left and right fractional derivative operators. By using the mountain pass theorem and the genus properties in critical point theory, we get some new results on…

In this work, we study the existence of weak solution to the following quasi linear elliptic problem involving the fractional $p$-Laplacian operator, a Hardy potential and multiple critical Sobolev nonlinearities with singularities,…

The main goal of this paper is to introduce a new fractional anisotropic Sobolev space with variable exponent where the basic qualitative properties (completeness, separability, reflexivity, ...) are established, including the continuous…

We extend the results of [5], where we proved an equivalence between weighted Poincar\'e inequalities and the existence of weak solutions to a family of Neumann problems related to a degenerate $p$-Laplacian. Here we prove a similar…

This paper concerns the existence of normalized solutions to a class of $(2,q)$-Laplacian equations with a power type nonlinearity in the intermediate regime between the two mass critical exponents $2(1+2/N)$, $q(1+2/N)$. More precisely, we…

We obtain nontrivial solutions for two types of critical $p$-Laplacian problems with asymmetric nonlinearities in a smooth bounded domain in ${\mathbb R}^N,\, N \ge 2$. For $p < N$, we consider an asymmetric problem involving the critical…

In the present work we briefly explain how to adapt techniques already used in fractional and $p$-fractional Laplacian cases to obtain the existence of a nontrivial solution at the mountain pass level and a nontrivial ground state solution,…

Using a variational technique we guarantee the existence of a solution to the \emph{resonant Lane-Emden} problem $-\Delta_p u=\lambda |u|^{q-2}u$, $u|_{\partial\Omega}=0$ if and only if a solution to $-\Delta_p u=\lambda |u|^{q-2}u+f$,…

For a generalization of the Gellerstedt operator with Dirichlet boundary conditions in a Tricomi domain. We establish Poho\v{z}aev-type identities and prove the nonexistence of nontrivial regular solutions. Furthermore, we investigate the…

We are concerned with the study of the existence and multiplicity of solutions for Dirichlet boundary value problems involving the (p(x), q(x))-equation and the nonlinearity is superlinear but does not satisfy the usual…

Let $\Omega$ be a bounded domain in $\mathbb{R}^N$. In this paper, we consider the following nonlinear elliptic equation of $N$-Laplacian type: $-\Delta_{N}u=f(x,u)$ where $u\in W_{0}^{1,2}\{0}$ when $f$ is of subcritical or critical…

We deal with existence and multiplicity results for the following nonhomogeneous and homogeneous equations, respectively: \begin{eqnarray*} (P_g)\quad - \Delta_{\lambda} u + V(x) u = f(x,u)+g(x),\;\mbox{ in } \R^N,\; \end{eqnarray*} and…

This paper is concerned with existence results for the singular $p$-biharmonic problem involving the Hardy potential and the critical Hardy-Sobolev exponent. More precisely, by using variational methods combined with the Mountain pass…

This work is devoted to study the existence of infinitely many weak solutions to nonlocal equations involving a general integrodifferential operator of fractional type. These equations have a variational structure and we find a sequence of…

We study a semilinear elliptic equation with a pure power nonlinearity with exponent $p>1$, and provide sufficient conditions for the existence of positive solutions. These conditions involve expected exit times from the domain, $D$, where…

We study fourth-order quasilinear elliptic problems that involve the p-biharmonic operator and Navier boundary conditions. The nonlinear term grows at the critical Sobolev rate. Starting from a Hamiltonian system of two second-order…

In this paper we consider nonlinear elliptic PDEs of the type $$-\Delta_p u+a(x)|u|^{p-2}u=|u|^{p^*-2}u \qquad \mbox{ in }\Omega,$$ where $1<p<N$ and $p^*=Np/(N-p)$ is the critical Sobolev exponent, and allowing the asymptotic behavior of…

In this paper we study nonlinear second-order differential inclusions involving the ordinary vector $p$-Laplacian, a multivalued maximal monotone operator and nonlinear multivalued boundary conditions. Our framework is general and unifying…

This paper is concerned with the following fractional Schr\"{o}dinger equations involving critical exponents: \begin{eqnarray*} (-\Delta)^{\alpha}u+V(x)u=k(x)f(u)+\lambda|u|^{2_{\alpha}^{*}-2}u\quad\quad \mbox{in}\ \mathbb{R}^{N},…