Related papers: (p,q)-Equations with singular and concave convex n…

We study the existence and non-existence of positive solutions for the $(p,q)$-Laplace equation $-\Delta_p u -\Delta_q u = \alpha |u|^{p-2} u + \beta |u|^{q-2} u$, where $p \neq q$, under the zero Dirichlet boundary condition in $\Omega$.…

We consider a nonlinear Dirichlet problem driven by the $p$-Laplace differential operator with a reaction which has a subcritical growth restriction only from above. We prove two multiplicity theorems producing three nontrivial solutions,…

Existence of solutions to an obstacle $p$-Laplacian problem exhibiting a singular, discontinuous reaction is proved. The reaction term may be discontinuous in a Lebesgue-negligible set. Moreover, solutions are shown to be locally…

In this paper, we analyze an eigenvalue problem for nonlinear elliptic operators involving homogeneous Dirichlet boundary conditions in a open smooth bounded domain. We prove bifurcation results from trivial solutions and from infinity for…

The existence of positive solutions is considered for the Dirichlet problem \[ \left\{ \begin{array} [c]{rcll}% -\Delta_{p}u & = & \lambda\omega_{1}(x)\left\vert u\right\vert ^{q-2}% u+\beta\omega_{2}(x)\left\vert u\right\vert…

We study the global structure of the set of radial solutions of a nonlinear Dirichlet problem involving the p-Laplacian with p>2, in the unit ball of $R^N$, $N \ges 1$. We show that all non-trivial radial solutions lie on smooth curves of…

We prove a bifurcation result for a Dirichlet problem driven by the fractional $p$-Laplacian (either degenerate or singular), in which the reaction is the difference between two sublinear powers of the unknown. In our argument, a…

In this paper we consider the existence of positive solutions for a singular elliptic problem involving an asymtotically linear nonlinearity and depending on one positive parameter. Using variational methods, together with comparison…

In this paper, we are interested in studying the multiplicity, uniqueness, and nonexistence of solutions for a class of singular elliptic eigenvalue problem for the Dirichlet fractional $(p,q)$-Laplacian. The nonlinearity considered…

We consider a Neumann boundary value problem driven by the anisotropic $(p,q)$-Laplacian plus a parametric potential term. The reaction is ``superlinear". We prove a global (with respect to the parameter) multiplicity result for positive…

In this paper, we consider a quasi-linear Dirichlet system with possible competing $(p,q)$-Laplacians and convections. Due to the lack of ellipticity, monotonicity, and variational structure, the standard approaches to the existence of weak…

We study the existence and multiplicity of positive solutions for the following concave-critical problem driven by an operator of mixed order obtained by the sum of the classical $p$-Laplacian and of the fractional $p$-Laplacian,…

This paper is devoted to the existence and non-existence of positive solutions for a $(p, q)$-Laplacian system with indefinite nonlinearity depending on two parameters $(\lambda,\mu)$. By using the sub-supersolution method together with…

We investigate the following fractional $p$-Laplacian equation \[ \begin{cases} \begin{aligned} (-\Delta)_p^s u&=\lambda |u|^{q-2}u+|u|^{p_s^*-2}u &&\text{in}~\Omega,\\ u &=0 &&\text{in}~ \mathbb{R}^n\setminus\Omega, \end{aligned}…

We investigate the existence of a curve $q\mapsto u_{q}$, with $q\in(0,1)$, of positive solutions for the problem $(P_{a,q})$: $-\Delta u=a(x)u^{q}$ in $\Omega$, $u=0$ on $\partial\Omega$, where $\Omega$ is a bounded and smooth domain of…

We study a nonlinear elliptic equation driven by the degenerate fractional p-Laplacian, with Dirichlet type condition and a jumping reaction, i.e., (p-1)-linear both at infinity and at zero but with different slopes crossing the principal…

We investigate the existence of nodal (sign-changing) solutions to the Dirichlet problem for two-parametric family of partially homogeneous $(p,q)$-Laplace equations $-\Delta_p u -\Delta_q u=\alpha |u|^{p-2}u+\beta |u|^{q-2}u$ where $p \neq…

We establish uniqueness results for quasilinear elliptic problems through the criterion recently provided in \cite{DFMST}. We apply it to generalized $p$-Laplacian subhomogeneous problems that may admit multiple nontrivial nonnegative…

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 investigate a nonlinear nonlocal eigenvalue problem involving the sum of fractional $(p,q)$-Laplace operators $(-\Delta)_p^{s_1}+(-\Delta)_q^{s_2}$ with $s_1,s_2\in (0,1)$; $p,q\in(1,\infty)$ and subject to Dirichlet boundary conditions…