1,720,981 research outputs found
On the Schrodinger equation in under the effect of a general nonlinear term
No full textIn this paper we prove the existence of a positive solution to the
equation in \RN, assuming the general
hypotheses on the nonlinearity introduced by Berestycki \&
Lions. Moreover we show that a minimizing problem, related to the existence of a ground state, has no solution
On a “zero mass” nonlinear Schrödinger equation
No full textWe look for positive solutions to the nonlinear Schr ̈odinger equation
−\varepsilon^2\Delta u − V (x)f'(u) = 0
in RN, where V is a continuous bounded positive potential and f satisfies particular growth
conditions which make our problem fall in the so called “zero mass case”. We prove an
existence result for any \varepsilon > 0, and a multiplicity result for \varepsilon sufficiently small
Ground state solutions for the nonlinear Klein-Gordon-Maxwell equations
No full textIn this paper we prove the existence of a ground state solution
for the nonlinear Klein–Gordon–Maxwell equations in the electrostatic case
Quasilinear elliptic equations in R^N via variational methods and Orlicz-Sobolev embeddings
No full textIn this paper we prove the existence of a nontrivial non-negative radial solution for
the quasilinear elliptic problem
\begin{equation*}\label{eq}
\left\{
\begin{array}{ll}
-\n \cdot \left[\phi'(|\n u|^2)\n u \right] +|u|^{\a-2}u =|u|^{s-2} u, & x\in
\RN,
\\
u(x) \to 0 , \quad \hbox{as }|x|\to \infty,
\end{array}
\right.
\end{equation*}
where ,
behaves like for small and for large ,
, 1<\a\le p^* q'/p' and \max\{q,\a\}< s, being
and and the conjugate exponents, respectively, of and .
Our aim is to approach the problem variationally by using the tools
of critical points theory in an Orlicz-Sobolev space.
A multiplicity result is also given
Ground state solutions for the nonlinear Schrodinger-Maxwell equations
No full textIn this paper we study the nonlinear Schrödinger–Maxwell equations
−\Delta u + V (x)u +φu = |u|^{p−1}u in R3,
−\Delta φ = u^2 in R^3.
If V is a positive constant, we prove the existence of a ground state solution (u,φ) for 2 <
p < 5. The non-constant potential case is treated for 3 < p < 5, and V possibly unbounded
below. Existence and nonexistence results are proved also when the nonlinearity exhibits
a critical growth
Quasilinear elliptic equations in R^N via variational methods and Orlicz-Sobolev embeddings
No full textIn this paper we prove the existence of a nontrivial non-negative radial solution for the quasilinear elliptic problem
\begin{equation*}
\left\{
\begin{array}{ll}
-\n \cdot \left[\phi'(|\n u|^2)\n u \right] +|u|^{\a-2}u =|u|^{s-2} u, & x\in
\RN,
\\
u(x) \to 0 , \quad \hbox{as }|x|\to \infty,
\end{array}
\right.
\end{equation*}
where , behaves like for small and for large , , 1<\a\le p^* q'/p' and \max\{q,\a\}< s, being
and and the conjugate exponents, respectively, of and .
Our aim is to approach the problem variationally by using the tools
of critical points theory in an Orlicz-Sobolev space.
A multiplicity result is also given
Multiple critical points for a class of nonlinear functionals
No full textIn this paper, we prove a multiplicity result concerning the critical points of a class of functionals involving local and nonlocal nonlinearities. We apply our result to the nonlinear Schrödinger–Maxwell system in R3 and to the nonlinear elliptic Kirchhoff equation in RN assuming on the local nonlinearity the general hypotheses introduced by Berestycki and Lions
Locating the peaks of semilinear elliptic systems
No full textWe consider a system of weakly coupled singularly perturbed semilinear elliptic equations.
First, we obtain a Lipschitz regularity result for the associated ground energy function Σ
as well as representation formulas for the left and the right derivatives. Then, we show that
the concentration points of the solutions locate close to the critical points of Σ in the sense
of subdifferential calculu
- …
