Related papers: Critical concave convex Ambrosetti-Prodi type prob…

We adapt a technique of nonsmooth critical point theory developed by Degiovanni-Zani for a semilinear problem involving the Laplacian to the the case of the $p$-Laplacian. We suppose only coercivity conditions on the potential and impose no…

A class of Laplace transforms is examined to show that particular cases of this class are associated with production-destruction and reaction-diffusion problems in physics, study of differences of independently distributed random variables…

We consider the following problem $$(P) \begin{cases} -\Delta_{p}u= c(x)|u|^{q-1}u+\mu |\nabla u|^{p}+h(x) & \ \ \mbox{ in }\Omega, u=0 & \ \ \mbox{ on } \partial\Omega, \end{cases}$$ where $\Omega$ is a bounded set in $\mathbb{R}^{N}$…

We prove conditions for existence of analytical solutions for boundary value problems with the Hilfer fractional derivative, generalizing the commonly used Riemann-Liouville and Caputo operators. The boundary values, referred to in this…

We investigate Lagrangian duality for nonconvex optimization problems. To this aim we use the $\Phi$-convexity theory and minimax theorem for $\Phi$-convex functions. We provide conditions for zero duality gap and strong duality. Among the…

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…

The main goal of this work is to prove the existence of three different solutions (one positive, one negative and one with nonconstant sign) for the equation $(-\Delta_p)^s u= |u|^{p^{*}_s -2} u +\lambda f(x,u)$ in a bounded domain with…

We establish the existence of a fully nontrivial solution with nonnegative components for a weakly coupled competitive system for the $p$-Laplacian in $\mathbb{R}^N$ whose nonlinear terms are purely critical. We also show that the purely…

We prove the existence of ground state positive solutions for a class of semipositone $p$-Laplacian problems with a critical growth reaction term. The proofs are established by obtaining crucial uniform $C^{1,\alpha}$ a priori estimates and…

We investigate the fractional magnetic $p$-Laplacian operator in the physical dimension case $N=3$, with $0<s<1<p$ and $sp<3$. Our goal is twofold. First, we define and study suitable functional settings for such operator proving…

We study a nonlinear elliptic boundary value problem defined on a smooth bounded domain involving the fractional Laplace operator, a concave-convex powers term together with mixed Dirichlet-Neumann boundary conditions.

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 study the local boundedness of local weak solutions to the following parabolic equation associated with fractional $p$-Laplacian type operators $$ \partial_t…

We investigate the existence of two nontrivial solutions for a poly-Laplacian system involving concave-convex nonlinearities and parameters with Dirichlet boundary condition on locally finite graphs. By using the mountain pass theorem and…

In this paper, we investigate the existence of multiple periodic solutions for two classes of nonlinear difference systems involving $(\phi_1,\phi_2)$-Laplacian. First, by using an important critical point theorem due to B. Ricceri, we…

We study the existence of positive solutions for the system of fractional elliptic equations of the type, \begin{equation*} \begin{array}{rl} (-\Delta)^{\frac{1}{2}} u &=\frac{p}{p+q}\lambda f(x)|u|^{p-2}u|v|^q + h_1(u,v)…

In this paper, we study the following critical system with fractional Laplacian: \begin{equation*} \begin{cases} (-\Delta)^{s}u= \mu_{1}|u|^{2^{\ast}-2}u+\frac{\alpha\gamma}{2^{\ast}}|u|^{\alpha-2}u|v|^{\beta} \ \ \ \text{in} \ \…

In this paper we extend the well-known concentration -- compactness principle for the Fractional Laplacian operator in unbounded domains. As an application we show sufficient conditions for the existence of solutions to some critical…

This paper gives an existence result for solutions to an elliptic optimal control problem based on a general fractional kernel, where the admissible controls come from a class satisfying both a growth bound and a superlinear-subcritical…

Given $n \geq 2$ and $1<p<n$, we consider the critical $p$-Laplacian equation $\Delta_p u + u^{p^*-1}=0$, which corresponds to critical points of the Sobolev inequality. Exploiting the moving planes method, it has been recently shown that…