Results 21 to 30 of about 2,557 (109)

Sign-Changing Solutions of Fractional 𝑝-Laplacian Problems

Advanced Nonlinear Studies, 2019
In this paper, we obtain the existence and multiplicity of sign-changing solutions of the fractional p-Laplacian problems by applying the method of invariant sets of descending flow and minimax theory.
Chang Xiaojun, Nie Zhaohu, Wang Zhi-Qiang   +2 more
doaj   +1 more source

On singular quasilinear elliptic equations with data measures

Advances in Nonlinear Analysis, 2021
The aim of this work is to study a quasilinear elliptic equation with singular nonlinearity and data measure. Existence and non-existence results are obtained under necessary or sufficient conditions on the data, where the main ingredient is the ...
Alaa Nour Eddine, Aqel Fatima, Taourirte Laila   +2 more
doaj   +1 more source

A finite‐dimensional reduction method for slightly supercritical elliptic problems

Abstract and Applied Analysis, Volume 2004, Issue 8, Page 683-689, 2004., 2004
We describe a finite‐dimensional reduction method to find solutions for a class of slightly supercritical elliptic problems. A suitable truncation argument allows us to work in the usual Sobolev space even in the presence of supercritical nonlinearities: we modify the supercritical term in such a way to have subcritical approximating problems; for ...
Riccardo Molle, Donato Passaseo
wiley   +1 more source

Solvability of nonlinear Dirichlet problem for a class of degenerate elliptic equations

Abstract and Applied Analysis, Volume 2004, Issue 3, Page 205-214, 2004., 2004
We prove an existence result for solution to a class of nonlinear degenerate elliptic equation associated with a class of partial differential operators of the form Lu(x)=∑i,j=1nDj(aij(x)Diu(x)), with Dj = ∂/∂xj, where aij : Ω → ℝ are functionssatisfying suitable hypotheses.
Albo Carlos Cavalheiro
wiley   +1 more source

Singular measure as principal eigenfunction of some nonlocal operators

, 2013
In this paper, we are interested in the spectral properties of the generalised principal eigenvalue of some nonlocal operator. That is, we look for the existence of some particular solution $(\lambda,\phi)$ of a nonlocal operator. $$\int_{\O}K(x,y)\phi(y)
Coville, Jerome
core   +1 more source

Fractional Hardy-Sobolev equations with nonhomogeneous terms

Advances in Nonlinear Analysis, 2021
This paper deals with existence and multiplicity of positive solutions to the following class of nonlocal equations with critical nonlinearity:
Bhakta Mousomi, Chakraborty Souptik, Pucci Patrizia   +2 more
doaj   +1 more source

Symmetry and concentration behavior of ground state in axially symmetric domains

Abstract and Applied Analysis, Volume 2004, Issue 12, Page 1019-1030, 2004., 2004
We let Ω(r) be the axially symmetric bounded domains which satisfy some suitable conditions, then the ground‐state solutions of the semilinear elliptic equation in Ω(r) are nonaxially symmetric and concentrative on one side. Furthermore, we prove the necessary and sufficient condition for the symmetry of ground‐state solutions.
Tsung-Fang Wu
wiley   +1 more source

Existence of Solutions for a Nonlinear Dirichlet Problem Involving Gradient Dependent Lipschitz Convection Function

Journal of Mathematics, Volume 2025, Issue 1, 2025.
In this paper, our goal is to prove the existence of a weak solution (in H01Ω) for a fully nonlinear Dirichlet problem with a nonmonotone (e.g., Lipschitz) convection function F that depends on ∇u, and a nonlinearity G that is not necessarily monotone and depends on the solution function u, and the higher order term is −ΔΓ(x, u) − diva(x, u, ∇u ...
Teffera M. Asfaw, Anteneh T. Adimasu, Achamyelesh A. Aligaz, Pramita Mishra   +3 more
wiley   +1 more source

The eigenvalue problem for the p‐Laplacian‐like equations

International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 9, Page 575-586, 2003., 2003
We consider the eigenvalue problem for the following p‐Laplacian‐like equation: −div(a(|Du|p)|Du|p−2Du) = λf(x, u) in Ω, u = 0 on ∂Ω, where Ω ⊂ ℝn is a bounded smooth domain. When λ is small enough, a multiplicity result for eigenfunctions are obtained. Two examples from nonlinear quantized mechanics and capillary phenomena, respectively, are given for
Zu-Chi Chen, Tao Luo
wiley   +1 more source

Operators with Polynomial Coefficients and Generalized Gelfand-Shilov Classes [PDF]

, 2012
2010 Mathematics Subject Classification: Primary 35S05, 35J60; Secondary 35A20, 35B08, 35B40.We study the problem of the global regularity for linear partial differential operators with polynomial coefficients.
Calvo, Daniela, De Donno, Giuseppe, Rodino, Luigi   +2 more
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