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Teodora Liliana Dinu

Publications and source records attributed to Teodora Liliana Dinu.

8 recordsLinked to original sources
arXiv2005

Entire solutions of Schrödinger elliptic systems with discontinuous nonlinearity and sign-changing potential

We establish the existence of an entire solution for a class of stationary Schrödinger systems with subcritical discontinuous nonlinearities and lower bounded potentials that blow-up at infinity. The proof is based on the critical point theory in the sense of Clarke and we apply Chang's version of the Mountain Pass Lemma for locally Lipschitz functionals. Our result generalizes in a nonsmooth framework a result of Rabinowitz \cite{rabi} related to entire solutions of the Schrödinger equation.

math.AP↗
arXiv2005

Nonlinear eigenvalue problems in Sobolev spaces with variable exponent

We study the boundary value problem $-{\rm div}((|\nabla u|^{p\_1(x) -2}+|\nabla u|^{p\_2(x)-2})\nabla u)=f(x,u)$ in $Ω$, $u=0$ on $\partialΩ$, where $Ω$ is a smooth bounded domain in $\RR^N$. We focus on the cases when $f\_\pm (x,u)=\pm(-λ|u|^{m(x)-2}u+|u|^{q(x)-2}u)$, where $m(x):=\max\{p\_1(x),p\_2(x)\} < q(x) < \frac{N\cdot m(x)}{N-m(x)}$ for any $x\in\barΩ$. In the first case we show the existence of infinitely many weak solutions for any $λ>0$. In the second case we prove that if $λ$ is large enough then there exists a nontrivial weak solution. Our approach relies on the variable exponent theory of generalized Lebesgue-Sobolev spaces, combined with a $\ZZ\_2$-symmetric version for even functionals of the Mountain Pass Lemma and some adequate variational methods.

math.AP↗
arXiv2005

Entire solutions of the nonlinear eigenvalue logistic problem with sign-changing potential and absorbtion

We are concerned with positive solutions decaying to zero at infinity for the logistic equation $-Δu=λ(V(x)u-f(u))$ in $\RR^N$, where $V(x)$ is a variable potential that may change sign, $λ$ is a real parameter, and $f$ is an absorbtion term such that the mapping $f(t)/t$ is increasing in $(0,\infty)$. We prove that there exists a bifurcation non-negative number $Λ$ such that the above problem has exactly one solution if $λ>Λ$, but no such a solution exists provided $λ\leqΛ$.

math.AP↗
arXiv2005

Entire positive solutions of the singular Emden-Fowler equation with nonlinear gradient term

Let $p$ and $q$ be locally Hölder functions in $\RR^N$, $p>0$ and $q\geq 0$. We study the Emden-Fowler equation $-Δu+ q(x)|\nabla u|^a=p(x)u^{-γ}$ in $\RR^N$, where $a$ and $γ$ are positive numbers. Our main result establishes that the above equation has a unique positive solutions decaying to zero at infinity. Our proof is elementary and it combines the maximum principle for elliptic equations with a theorem of Crandall, Rabinowitz and Tartar.

math.AP↗
arXiv2005

Subcritical perturbations of resonant linear problems with sign-changing potential

We establish existence and multiplicity theorems for a Dirichlet boundary value problem at resonance, which is a nonlinear subcritical perturbation of a linear eigenvalue problem studied by Cuesta. Our framework includes a sign-changing potential and we locate the solutions by using the Mountain Pass lemma and the Saddle Point theorem.

math.AP↗
arXiv2005

Entire solutions of sublinear elliptic equations in anisotropic media

We study the nonlinear elliptic problem $-Δu=ρ(x)f(u)$ in $\RR^N$ ($N\geq 3$), $\lim\_{|x|\ri\infty}u(x)=\ell$, where $\ell\geq 0$ is a real number, $ρ(x)$ is a nonnegative potential belonging to a certain Kato class, and $f(u)$ has a sublinear growth. We distinguish the cases $\ell>0$ and $\ell=0$ and we prove existence and uniqueness results if the potential $ρ(x)$ decays fast enough at infinity. Our arguments rely on comparison techniques and on a theorem of Brezis and Oswald for sublinear elliptic equations.

math.AP↗
arXiv2005

Entire solutions of multivalued nonlinear Schrodinger equations in Sobolev spaces with variable exponent

We establish the existence of an entire solution for a class of stationary Schrödinger equations with subcritical discontinuous nonlinearity and lower bounded potential that blows-up at infinity. The abstract framework is related to Lebesgue-Sobolev spaces with variable exponent. The proof is based on the critical point theory in the sense of Clarke and we apply Chang's version of the Mountain Pass Lemma without the Palais-Smale condition for locally Lipschitz functionals. Our result generalizes in a nonsmooth framework a result of Rabinowitz on the existence of ground-state solutions of the nonlinear Schrödinger equation.

math.AP↗