Related papers: Multiple solutions for Dirichlet nonlinear BVPs in…
In this paper we present some very recent results regarding existence, uniqueness, and multiplicity of solutions for quasilinear elliptic equations and systems, exhibiting both singular and convective reaction terms. The importance of…
We investigate the existence and multiplicity of solutions for higher order discrete boundary value problems via critical point theory.
The present paper is concerned with the Cauchy-Dirichlet problem for fractional (and non-fractional) nonlinear diffusion equations posed in bounded domains. Main results consist of well-posedness in an energy class with no sign restriction…
We study singular solutions to the fractional Laplace equation and, more generally, to nonlocal linear equations with measurable kernels. We establish B\^ocher type results that characterize the behavior of singular solutions near the…
In this paper, we investigate the existence of positive weak solutions to a nonlocal singular elliptic problem under Dirichlet boundary condition. Problem is settled in fractional Musielak-Sobolev spaces with variable order. The main tool…
In this paper, we use bifurcation method to investigate the existence and multiplicity of one-sign solutions of the $p$-Laplacian involving a linear/superlinear nonlinearity with zeros. To do this, we first establish a bifurcation theorem…
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 establish the existence of multiple solutions for singular quasilinear elliptic problems with a precise sign information: two opposite constant sign solutions and a nodal solution. The approach combines sub-supersolutions method and…
Initial-boundary value problems for second order fully nonlinear PDEs with Caputo time fractional derivatives of order less than one are considered in the framework of viscosity solution theory. Associated boundary conditions are Dirichlet…
In this paper, we consider a p-Laplacian equation in {R}^{N}with sign-changing potential and subcritical p-superlinear nonlinearity. By using the cohomological linking method for cones developed by Degiovanni and Lancelotti in 2007, an…
We obtain, by using the Leggett-Williams fixed point theorem, sufficient conditions that ensure the existence of at least three positive solutions to some $p$-Laplacian boundary value problems on time scales.
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 consider a Dirichlet type problem for a nonlinear, nonlocal equation driven by the degenerate fractional p-Laplacian, with a logistic type reaction depending on a positive parameter. In the subdiffusive and equidiffusive cases, we prove…
By using a specially constructed cone and the fixed point index theory, this paper investigates the existence of multiple positive solutions for the third-order three-point singular semipositone BVP: $\begin{cases} x'''(t)-\ld f(t,x) =0,…
This paper is concerned with a nonlinear Steklov boundary-value problem involving weighted $p(.)$-Laplacian. Using the Ricceri's variational principle, we obtain the existence of at least three weak solutions in double weighted variable…
We construct a self-similar solution of the heat equation for the fractional Laplacian with Dirichlet boundary conditions in every fat cone. As applications, we give the Yaglom limit and entrance law for the corresponding killed isotropic…
This paper aims to investigate the existence and uniqueness of solutions for a sixth order differential equation involving nonlocal and integral boundary conditions. Firstly, we obtain the properties of the relevant Green's functions. The…
This manuscript investigates the existence and uniqueness of solutions to the first order fractional anti-periodic boundary value problem involving Caputo-Katugampola (CK) derivative. A variety of tools for analysis this paper through the…
We establish several results related to existence, nonexistence or bifurcation of positive solutions for a Dirichlet boundary value problem with in a smooth bounded domain. The main feature of this paper consists in the presence of a…
We address the existence in the sense of sequences of solutions for a certain integro-differential type problem involving the logarithmic Laplacian. The argument is based on the fixed point technique when such equation contains the operator…