Related papers: The One-Phase Bifurcation For The p-Laplacian
We obtain the existence of mountain pass solutions for quasi-linear equations without the typical assumptions which guarantee the boundedness of an arbitrary Palais-Smale sequence. This is done through a recent version of the monotonicity…
The paper deals with the existence and uniqueness of a non-trivial solution to non-homogeneous $ p ( x ) -$laplacian equations, managed by non polynomial growth operator in the framework of variable exponent Sobolev spaces on Riemannian…
We study a Dirichlet problem driven by the degenerate fractional p-Laplacian and involving a nonlinear reaction, which depends on a positive parameter. The reaction is assumed to be (p-1)-sublinear near the origin and (p-1)-superlinear at…
We present existence and nonexistence results on the solution of an overdetermined problem for the normalized p-Laplacian in a bounded open set, with p ranging from 1 to infinity. More precisely we consider a non-constant Neumann condition…
We consider viscosity solutions to a one-phase free boundary problem for the $p(x)$-Laplacian with non-zero right hand side. We apply the tools developed in \cite{D} to prove that flat free boundaries are $C^{1,\alpha}$. Moreover, we obtain…
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…
In this paper we are concerned with a two phase boundary obstacle-type problem for the bi-Laplace operator in the upper unit ball. The problem arises in connection with unilateral phenomena for flat elastic plates. It can also be seen as an…
In this paper we study double phase problems with nonlinear boundary condition and gradient dependence. Under quite general assumptions we prove existence results for such problems where the perturbations satisfy a suitable behavior in the…
We revisit a textbook example of a singularly perturbed nonlinear boundary-value problem. Unexpectedly, it shows a wealth of phenomena that seem to have been overlooked previously, including a pitchfork bifurcation in the number of…
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…
This paper is concerned with an evolution problem having an elliptic equation involving the 1-Laplacian operator and a dynamical boundary condition. We apply nonlinear semigroup theory to obtain existence and uniqueness results as well as a…
We prove that an a priori BMO gradient estimate for the two phase singular perturbation problem implies Lipschitz regularity for the limits. This problem arises in the mathematical theory of combustion where the reaction-diffusion is…
In this paper, we investigate existence results for nonlinear nonlocal problems governed by an operator obtained as a superposition of fractional $p$-Laplacians, subject to Neumann boundary conditions. A spectral analysis of the main…
In the present paper we deal with a quasilinear problem involving a singular term and a parametric superlinear perturbation. We are interested in the existence, nonexistence and multiplicity of positive solutions as the parameter…
We study certain significant properties of the equilibrium configurations of a rigid body subject to an undamped elastic restoring force, in the stream of a viscous liquid in an unbounded 3D domain. The motion of the coupled system is…
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 work, we study the existence and multiplicity of solutions for the following problem \begin{equation}\label{probaa1} \left\{ \begin{aligned} -(\Delta)_{p}^{s} u + V(x)|u|^{p-2}u &= \lambda f(u),&x\in\Omega; u&=0,&x\in…
We show an abstract time-periodic bifurcation theorem in Banach spaces. The key point as well as the novelty of the method is to split the original evolution equation into two different coupled equations, one for the time-average of the…
Existence of two solutions to a parametric singular quasi-linear elliptic problem is proved. The equation is driven by the {\Phi}-Laplacian operator and the reaction term can be non-monotone. The main tools employed are a local minimum…
In this paper, we prove the existence of a weak solution for the Dirichlet boundary value problem related to the $p(x)-$Laplacian $$ -\mbox{div}(|\nabla u|^{p(x)-2}\nabla u)+u\in -[\underline{g}(x,u),\overline{g}(x,u)], $$ by using the…