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Search Results: 1 - 10 of 5776 matches for " Simone Secchi "
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Increasing variational solutions for a nonlinear $p$-laplace equation without growth conditions
Simone Secchi
Mathematics , 2010,
Abstract: By means of a recent variational technique, we prove the existence of radially monotone solutions to a class of nonlinear problems involving the $p$-Laplace operator. No subcriticality condition (in the sense of Sobolev spaces) is required.
Ground state solutions for nonlinear fractional Schr?dinger equations in $\mathbb{R}^N$
Simone Secchi
Mathematics , 2012, DOI: 10.1063/1.4793990
Abstract: We construct solutions to a class of Schr\"{o}dinger equations involving the fractional laplacian. Our approach is variational in nature, and based on minimization on the Nehari manifold.
Perturbation results for some nonlinear equations involving fractional operators
Simone Secchi
Mathematics , 2012,
Abstract: By using a perturbation technique in critical point theory, we prove the existence of solutions for two types of nonlinear equations involving fractional differential operators.
On fractional Schr?dinger equations in (\mathbb{R}^N) without the Ambrosetti-Rabinowitz condition
Simone Secchi
Mathematics , 2012,
Abstract: In this note we prove the existence of radially symmetric solutions for a class of fractional Schr\"odinger equation in (\mathbb{R}^N) of the form {equation*} \slap u + V(x) u = g(u), {equation*} where the nonlinearity $g$ does not satisfy the usual Ambrosetti-Rabinowitz condition. Our approach is variational in nature, and leans on a Pohozaev identity for the fractional laplacian.
Nonlinear differential equations on non-compact domains
Simone Secchi
Mathematics , 2002,
Abstract: We present some results in the analysis of non-compact differential equations on unbounded domains.
A note on Schr?dinger--Newton systems with decaying electric potential
Simone Secchi
Mathematics , 2009,
Abstract: We prove the existence of solutions for the singularly perturbed Schr\"odinger--Newton system {ll} \hbar^2 \Delta \psi - V(x) \psi + U \psi =0 \hbar^2 \Delta U + 4\pi \gamma |\psi|^2 =0 . \hbox{in $\mathbb{R}^3$} with an electric potential (V) that decays polynomially fast at infinity. The solution $\psi$ concentrates, as $\hbar \to 0$, around (structurally stable) critical points of the electric potential. As a particular case, isolated strict extrema of (V) are allowed.
On some nonlinear fractional equations involving the Bessel operator
Simone Secchi
Mathematics , 2015,
Abstract: Under different assumptions on the potential functions $b$ and $c$, we study the fractional equation $\left( I-\Delta \right)^{\alpha} u = \lambda b(x) |u|^{p-2}u+c(x)|u|^{q-2}u$ in $\mathbb{R}^N$. Our existence results are based on compact embedding properties for weighted spaces.
A Note on Closed Geodesics for a Class of non-compact Riemannian Manifolds
Simone Secchi
Mathematics , 2000,
Abstract: We prove the existence of multiple closed geodesics on non-compact cylindrica manifolds.
The Brezis--Nirenberg problem for the Hénon equation: ground state solutions
Simone Secchi
Mathematics , 2012,
Abstract: This work is devoted to the Dirichlet problem for the equation (-\Delta u = \lambda u + |x|^\alpha |u|^{2^*-2} u) in the unit ball of $\mathbb{R}^N$. We assume that $\lambda$ is bigger than the first eigenvalues of the laplacian, and we prove that there exists a solution provided $\alpha$ is small enough. This solution has a variational characterization as a ground state.
Interior spikes of a singularly perturbed Neumann problem with potentials
Alessio Pomponio,Simone Secchi
Mathematics , 2003,
Abstract: In this paper we prove that a singularly perturbed Neumann problem with potentials admits the existence of interior spikes concentrating in maxima and minima of an auxiliary function depending only on the potentials.
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