Results 61 to 70 of about 429 (89)

Existence results for double-phase problems via Morse theory [PDF]

arXiv, 2016
We obtain nontrivial solutions for a class of double-phase problems using Morse theory. In the absence of a direct sum decomposition, we use a cohomological local splitting to get an estimate of the critical groups at zero.
arxiv  

Increased mortality risk for adults aged 25-44 years with long-term disability: A prospective cohort study with a 35-year follow-up of 30,080 individuals from 1984-2019 in the population-based HUNT study. [PDF]

Lancet Reg Health Eur, 2022
Langballe EM, Tangen GG, Engdahl B, Strand BH.   +3 more
europepmc   +1 more source

A Fractional Free Boundary Problem Related to a Plasma Problem [PDF]

arXiv, 2015
We study a fractional analogue of a plasma problem arising from physics. Specifically, for a fixed bounded domain $\Omega$ we study solutions to the eigenfunction equation \[ (- \Delta)^s u = \lambda(u- \gamma)_+ \] with $u \equiv 0$ on $\partial \Omega$.
arxiv  

The second Yamabe invariant [PDF]

J. Funct. Anal. 235 no. 2, 377-412 (2006), 2005
Let $(M,g)$ be a compact Riemannian manifold of dimension $n \geq 3$. We define the second Yamabe invariant as the infimum of the second eigenvalue of the Yamabe operator over the metrics conformal to $g$ and of volume 1. We study when it is attained. As an application, we find nodal solutions of the Yamabe equation.
arxiv  

On an eigenvalue problem associated with the (p, q) − Laplacian

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica
Let Ω ⊂ ℝN, N ≥ 2, be a bounded domain with smooth boundary ∂Ω. Consider the following generalized Robin-Steklov eigenvalue problem associated with the operator 𝒜u = − Δpu − Δqu {𝒜u+ρ1(x)|u|p-2u+ρ2(x)|u|q-2u=λα(x)|u|r-2u,   x∈Ω,∂u∂vA+γ1(x)|u|p-2u+γ2(x)|u|
Barbu Luminiţa, Burlacu Andreea, Moroşanu Gheorghe   +2 more
doaj   +1 more source

Subcritical perturbations of resonant linear problems with sign-changing potential [PDF]

arXiv, 2005
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.
arxiv  

On a nonlinear eigenvalue problem in Sobolev spaces with variable exponent [PDF]

arXiv, 2005
We consider a class of nonlinear Dirichlet problems involving the $p(x)$--Laplace operator. Our framework is based on the theory of Sobolev spaces with variable exponent and we establish the existence of a weak solution in such a space. The proof relies on the Mountain Pass Theorem.
arxiv  

Exponential decay of eigenfunctions and generalized eigenfunctions of a non self-adjoint matrix Schrödinger operator related to NLS [PDF]

arXiv, 2007
We study the decay of eigenfunctions of the non self-adjoint matrix operator $\calH = (\begin{smallmatrix} -\Delta +\mu+U & W \W & \Delta -\mu -U \end{smallmatrix})$, for $\mu>0$, corresponding to eigenvalues in the strip $-\mu<\re E <\mu$.
arxiv  

On spectral minimal partitions: the case of the sphere [PDF]

arXiv, 2009
We consider spectral minimal partitions. Continuing work of the the present authors about problems for planar domains, [23], we focus on the sphere and obtain a sharp result for 3-partitions which is related to questions from harmonic analysis, in particular to a conjecture of Bishop.
arxiv  

Refined asymptotics for eigenvalues on domains of infinite measure [PDF]

arXiv, 2009
In this work we study the asymptotic distribution of eigenvalues in one-dimensional open sets. The method of proof is rather elementary, based on the Dirichlet lattice points problem, which enable us to consider sets with infinite measure. Also, we derive some estimates for the the spectral counting function of the Laplace operator on unbounded two ...
arxiv