Results 21 to 30 of about 41,085 (189)

Asymptotic profile and Morse index of nodal radial solutions to the H\'enon problem [PDF]

, 2018
We compute the Morse index of nodal radial solutions to the H\'enon problem \[\left\{\begin{array}{ll} -\Delta u = |x|^{\alpha}|u|^{p-1} u \qquad & \text{ in } B, \newline u= 0 & \text{ on } \partial B, \end{array} \right. \] where $B$ stands
Amadori, Anna Lisa, Gladiali, Francesca
core   +2 more sources

Ground state sign-changing solutions for semilinear Dirichlet problems

Boundary Value Problems, 2018
In the present paper, we consider the existence of ground state sign-changing solutions for the semilinear Dirichlet problem 0.1 {−△u+λu=f(x,u),x∈Ω;u=0,x∈∂Ω, $$ \left \{ \textstyle\begin{array}{l@{\quad}l} -\triangle u+\lambda u=f(x, u), & \hbox{$x\in ...
Xiaoyan Lin, Xianhua Tang
doaj   +1 more source

Nodal solutions for the Choquard equation [PDF]

, 2016
We consider the general Choquard equations $$ -\Delta u + u = (I_\alpha \ast |u|^p) |u|^{p - 2} u $$ where $I_\alpha$ is a Riesz potential. We construct minimal action odd solutions for $p \in (\frac{N + \alpha}{N}, \frac{N + \alpha}{N - 2})$ and ...
Ghimenti, Marco, Van Schaftingen, Jean
core   +2 more sources

Elementary excitation families and their frequency ordering in cylindrically symmetric Bose-Einstein condensates [PDF]

, 2001
We present a systematic classification of the elementary excitations of Bose-Einstein condensates in cylindrical traps in terms of their shapes. The classification generalizes the concept of families of excitations first identified by Hutchinson and ...
Patterson M.J., Soulas G. C., Soulas G. C.   +2 more
core   +2 more sources

Nonhomogeneous Hemivariational Inequalities with Indefinite Potential and Robin Boundary Condition

, 2017
We consider a nonlinear, nonhomogeneous Robin problem with an indefinite potential and a nonsmooth primitive in the reaction term. In fact, the right-hand side of the problem (reaction term) is the Clarke subdifferential of a locally Lipschitz integrand.
Papageorgiou, Nikolaos S., Repovš, Dušan D., Rădulescu, Vicenţiu D.   +2 more
core   +1 more source

A nonexistence result for sign-changing solutions of the Brezis-Nirenberg problem in low dimensions [PDF]

, 2015
We consider the Brezis-Nirenberg problem: \begin{equation*} \begin{cases} -\Delta u = \lambda u + |u|^{2^* -2}u & \hbox{in}\ \Omega\\ u=0 & \hbox{on}\ \partial \Omega, \end{cases} \end{equation*} where $\Omega$ is a smooth bounded domain in $\mathbb{R}^N$
Iacopetti, Alessandro, Pacella, Filomena
core   +4 more sources

Nonlinear Dirichlet problems with unilateral growth on the reaction

, 2019
We consider a nonlinear Dirichlet problem driven by the $p$-Laplace differential operator with a reaction which has a subcritical growth restriction only from above. We prove two multiplicity theorems producing three nontrivial solutions, two of constant
Papageorgiou, Nikolaos S., Repovš, Dušan D., Rădulescu, Vicenţiu D.   +2 more
core   +2 more sources

Constant sign and nodal solutions for anisotropic eigenvalue problems

Positivity
Abstract We consider a nonlinear eigenvalue problem driven by the anisotropic (p, q)-Laplacian. Using variational tools, truncations, comparisons and critical groups, we show that for all small values of the parameter, the problem has extremal constant sign solutions and nodal solutions. These solutions are ordered and vanish in
Öztürk, Eylem, Papageorgiou, Nikolaos S.   +1 more
openaire   +2 more sources

Noncoercive resonant (p,2)-equations with concave terms

Advances in Nonlinear Analysis, 2018
We consider a nonlinear Dirichlet problem driven by the sum of a p-Laplace and a Laplacian (a (p,2){(p,2)}-equation). The reaction exhibits the competing effects of a parametric concave term plus a Caratheodory perturbation which is resonant with respect
Papageorgiou Nikolaos S., Zhang Chao
doaj   +1 more source

Constant Sign and Nodal Solutions for Variable Exponent Double Phase Problem

Results in Mathematics
Let \(\Omega \subseteq \mathbb{R}^N\) (\(N \geq 2\)) be a bounded domain with Lipschitz boundary \(\partial \Omega\). The authors study the following nonlinear problem \[ - \Delta^a_p u - \Delta_q u = f(z,u) \mbox{ in }\Omega, \quad u\big|_{\partial \Omega}=0, \] in the case of variable exponents \(p,q \in C(\overline{\Omega})\) with \(1< q(x)
Failla, Giuseppe, Gasiński, Leszek, Papageorgiou, Nikolaos S.   +2 more
openaire   +1 more source