Related papers: Positive solutions for nonlinear Neumann problems …
In this paper, the existence of positive strong solutions to a Dirichlet $p$-Laplacian problem with reaction both singular at zero and highly discontinuous is investigated. In particular, it is only required that the set of discontinuity…
We consider a parametric semilinear Robin problem driven by the Laplacian plus an indefinite potential. The reaction term involves competing nonlinearities. More precisely, it is the sum of a parametric sublinear (concave) term and a…
We prove the existence of one positive, one negative, and one sign-changing solution of a $p$-Laplacian equation on $\mathbb{R}^N$, with a $p$-superlinear subcritical term. Sign-changing solutions of quasilinear elliptic equations set on…
A short account of some recent existence, multiplicity, and uniqueness results for singular p-Laplacian problems either in bounded domains or in the whole space is performed, with a special attention to the case of convective reactions. An…
We prove that quasi-concave positive solutions to a class of quasi-linear elliptic equations driven by the $p$-Laplacian in convex bounded domains of the plane have only one critical point. As a consequence, we obtain strict concavity…
The first nontrivial eigenfunction of the Neumann eigenvalue problem for the $p$-Laplacian, suitable normalized, converges as $p$ goes to $\infty$ to a viscosity solution of an eigenvalue problem for the $\infty$-Laplacian. We show among…
We study the existence of positive solutions for the following class of $(p,q)$-Laplacian coupled systems \[ \left\{ \begin{array}{lr} -\Delta_{p} u+a(x)|u|^{p-2}u=f(u)+ \alpha\lambda(x)|u|^{\alpha-2}u|v|^{\beta}, & x\in\mathbb{R}^{N},…
In this paper, we establish the results on the existence, nonexistence and multiplicity of positive solutions to singular boundary value problems involving $\varphi$-Laplacian. Our approach is based on the fixed point index theory. The…
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…
In this article, we consider the boundary-value problem of nonlinear fractional differential equation with p-Laplacian operator. By the properties of Green function and Schauder fixed point theorem, several existence and nonexistence…
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…
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…
We consider, for $a,l\geq1,$ $b,s,\alpha>0,$ and $p>q\geq1,$ the homogeneous Dirichlet problem for the equation $-\Delta_{p}u=\lambda u^{q-1}+\beta u^{a-1}\left\vert \nabla u\right\vert ^{b}+mu^{l-1}e^{\alpha u^{s}}$ in a smooth bounded…
We prove the existence of a positive solution to a semipositone $N$-Laplacian problem with a critical Trudinger-Moser nonlinearity. The proof is based on obtaining uniform $C^{1,\alpha}$ a priori estimates via a compactness argument. Our…
In this paper we develop a new theory for the existence, localization and multiplicity of positive solutions for a class of non-variational,quasilinear, elliptic systems. In order to do this, we provide a fairly general abstract framework…
We prove that a class of superlinear indefinite problems with homogeneous Neumann boundary conditions admits an arbitrarily high number of positive solutions, provided that the parameters of the problem are adequately chosen. The…
In this survey we report on some recent results related to various singular phenomena arising in the study of some classes of nonlinear elliptic equations. We establish qualitative results on the existence, nonexistence or the uniqueness of…
In the present paper we prove existence results for solutions to nonlinear elliptic Neumann problems whose prototype is \begin{equation*} \begin{cases} -\Delta_{p} u -\text{div} (c(x)|u|^{p-2}u)) =f & \text{in}\ \Omega, \\ \left( |\nabla…
In this work, we investigate the existence of positive solutions for a multi-point boundary value problem for a second order delay differential equation. Under certain growth conditions on the nonlinearity, and by the mean of Leray-Schauder…
In this paper we consider quasilinear elliptic equations with double phase phenomena and a reaction term depending on the gradient. Under quite general assumptions on the convection term we prove the existence of a weak solution by applying…