19,723 research outputs found
Existence of positive solution for a nonlinear elliptic equation with saddle-like potential and nonlinearity with exponential critical growth in
In this paper, we use variational methods to prove the existence of positive
solution for the following class of elliptic equation
-\epsilon^{2}\Delta{u}+V(z)u=f(u) \,\,\, \mbox{in} \,\,\, \mathbb{R}^{2},
where is a positive parameter, is a saddle-like potential and
has an exponential critical growth
Existence of heteroclinic solution for a double well potential equation in an infinite cylinder of
This paper concernes with the existence of heteroclinic solutions for the
following class of elliptic equations -\Delta{u}+A(\epsilon x, y)V'(u)=0,
\quad \mbox{in} \quad \Omega, where , \Omega=\R \times \D is
an infinite cylinder of with . Here, we have
considered a large class of potential that includes the Ginzburg-Landau
potential and two geometric conditions on the function
. In the first condition we assume that is asymptotic at infinity to a
periodic function, while in the second one satisfies
0Comment: In this revised version we have corrected some typos and changed the
proof of some lemma
Existence of standing waves solution for a Nonlinear Schr\"odinger equations in
In this paper, we investigate the existence of positive solution for the
following class of elliptic equation - \epsilon^{2}\Delta u +V(x)u= f(u)
\,\,\,\, \mbox{in} \,\,\, \mathbb{R}^{N}, where is a positive
parameter, has a subcritical growth and is a positive potential
verifying some conditions
Existence of solutions for a class of singular elliptic systems with convection term
We show the existence of positive solutions for a class of singular elliptic
systems with convection term. The approach combines pseudomonotone operator
theory, sub and supersolution method and perturbation arguments involving
singular terms
Existence of a positive solution for a logarithmic Schr\"{o}dinger equation with saddle-like potential
In this article we use the variational method developed by Szulkin
\cite{szulkin} to prove the existence of a positive solution for the following
logarithmic Schr\"{o}dinger equation \left\{ \begin{array}{lc}
-{\epsilon}^2\Delta u+ V(x)u=u \log u^2, & \mbox{in} \quad \mathbb{R}^{N}, \\
%u(x)>0, & \mbox{in} \quad \mathbb{R}^{N} \\ u \in H^1(\mathbb{R}^{N}), & \; \\
\end{array} \right. where and is a saddle-like
potential
Positive solutions for a class of quasilinear singular elliptic systems
In this paper we establish the existence of two positive solutions for a
class of quasilinear singular elliptic systems. The main tools are sub and
supersolution method and Leray-Schauder Topological degree.Comment: 19 page
Existence of positive multi-bump solutions for a Schr\"odinger-Poisson system in
In this paper we are going to study a class of Schr\"odinger-Poisson system
\left\{ \begin{array}{ll}
- \Delta u + (\lambda a(x)+1)u+ \phi u = f(u) \mbox{ in } \,\,\,
\mathbb{R}^{3},\\ -\Delta \phi=u^2 \mbox{ in } \,\,\, \mathbb{R}^{3}.\\
\end{array} \right. Assuming that the nonnegative function has a
potential well consisting of disjoint components
and the nonlinearity has a
subcritical growth, we are able to establish the existence of positive
multi-bump solutions by variational methods.Comment: arXiv admin note: text overlap with arXiv:1402.683
Existence of solutions for a nonlocal variational problem in with exponential critical growth
We study the existence of solution for the following class of nonlocal
problem, -\Delta u +V(x)u =\Big( I_\mu\ast F(x,u)\Big)f(x,u) \quad \mbox{in}
\quad \mathbb{R}^2, where is a positive periodic potential,
, and is the primitive function of
in the variable . In this paper, by assuming that the nonlinearity
has an exponential critical growth at infinity, we prove the existence
of solutions by using variational methods
Ground state solution for a class of indefinite variational problems with critical growth
In this paper we study the existence of ground state solution for an
indefinite variational problem of the type \left\{\begin{array}{l} -\Delta
u+(V(x)-W(x))u=f(x,u) \quad \mbox{in} \quad \R^{N}, u\in H^{1}(\R^{N}),
\end{array}\right. \eqno{(P)} where , and are
continuous functions verifying some technical conditions and possesses a
critical growth. Here, we will consider the case where the problem is
asymptotically periodic, that is, is -periodic, goes to 0
at infinity and is asymptotically periodic
Existence of multi-bump solutions for a class of elliptic problems involving the biharmonic operator
Using variational methods, we establish existence of multi-bump solutions for
the following class of problems
\left\{
\begin{array}{l}
\Delta^2 u +(\lambda V(x)+1)u = f(u), \quad \mbox{in} \quad \mathbb{R}^{N}, u
\in H^{2}(\mathbb{R}^{N}),
\end{array}
\right.
where , is the biharmonic operator, is a
continuous function with subcritical growth and is a continuous function verifying some conditions
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