A classification result for the quasi-linear Liouville equation [PDF]
arXiv, 2016 Entire solutions of the $n-$Laplace Liouville equation in $\mathbb{R}^n$ with finite mass are completely classified.
arxiv
Multiplicity of positive solutions for a critical quasilinear Neumann problem [PDF]
arXiv, 2016 We establish the multiplicity of positive solutions to a quasilinear Neumann problem in expanding balls and hemispheres with critical exponent in the boundary condition.
arxiv
Symmetry results for $p$-Laplacian systems involving a first order term [PDF]
arXiv, 2020 In this paper we obtain symmetry and monotonicity results for positive solutions to some $p$-Laplacian cooperative systems in bounded domains involving first order terms and under zero Dirichlet boundary condition.
arxiv
Some remarks on sign changing solutions of a quasilinear elliptic equation in two variables [PDF]
, 2012 We consider planar solutions to certain quasilinear elliptic equations subject to the Dirichlet boundary conditions; the boundary data is assumed to have finite number of relative maximum and minimum values.
Granlund, Seppo, Marola, Niko
core
The Expected Time to End the Tug-of-War in a Wedge [PDF]
arXiv, 2010 Using a solution of a nonhomogeneous partial differential equation involving the p- Laplacian, we study the finiteness of the expected time to end the tug-of-war in a wedge.
arxiv
Hölder continuity for the solutions of the p(x)-Laplace equation with general right-hand side [PDF]
arXiv, 2020 We show that bounded solutions of the quasilinear elliptic equation $\Delta_{p(x)} u=g+div(\textbf{F})$ are locally H\"{o}lder continuous provided that the functions $g$ and $\textbf{F}$ are in suitable Lebesgue spaces.
arxiv
An elliptic system with logarithmic nonlinearity
Advances in Nonlinear Analysis, 2017 In the present paper, we study the existence of solutions for some classes of singular systems involving the Δp(x){\Delta_{p(x)}} and Δq(x){\Delta_{q(x)}} Laplacian operators. The approach is based on bifurcation theory and the sub-supersolution method
Alves Claudianor +2 more
doaj +1 more source
The p-Laplacian with respect to measures [PDF]
arXiv, 2011 We introduce a definition for the $p$-Laplace operator on positive and finite Borel measures that satisfy an Adams-type embedding condition.
arxiv
Optimal Design Problems for the First p-Fractional Eigenvalue with Mixed Boundary Conditions
Advanced Nonlinear Studies, 2018 In this paper, we study an optimal shape design problem for the first eigenvalue of the fractional p-Laplacian with mixed boundary conditions. The optimization variable is the set where the Dirichlet condition is imposed (that is restricted to have ...
Fernández Bonder Julian +2 more
doaj +1 more source
Multiplicity of 1D-concentrating positive solutions to the Dirichlet problem for equation with $p$-Laplacian [PDF]
arXiv, 2012 We prove the multiplicity of spike-layer type solutions to the Dirichlet problem for the equation $-\Delta_p u = u^{q-1}$ in expanding annuli.
arxiv