Related papers: Quasilinear eigenvalues

In the paper we consider elliptic equations of the form $-Au=u^{-\gamma}\cdot\mu$, where $A$ is the operator associated with a regular symmetric Dirichlet form, $\mu$ is a positive nontrivial measure and $\gamma>0$. We prove the existence…

This paper studies a class of $p$-Laplace equations with cubic polynomial nonlinearity \[ \Delta_p v + (v-a_1)(v-a_2)(v-a_3) = 0 \] on complete Riemannian manifolds $M$ with lower Ricci curvature bounds, where $a_1 < a_2 < a_3$ are real…

Boundary value problems for a class of quasilinear elliptic equations, with an Orlicz type growth and L^1 right-hand side are considered. Both Dirichlet and Neumann problems are contemplated. Existence and uniqueness of generalized…

We study the discrete version of the $p$-Laplacian. Based on its variational properties we discuss some features of the associated parabolic problem. Our approach allows us in turn to obtain interesting information about positivity and…

In this paper we study variations of the first non-trivial eigenvalues of the two-dimensional $p$-Laplace operator, $p>2$, generated by measure preserving quasiconformal mappings $\varphi : \mathbb D\to\Omega$, $\Omega \subset\mathbb R^2$.…

We study the first nonzero eigenvalues for the $p$-Laplacian on quaternionic K\"ahler manifolds. Our first result is a lower bound for the first nonzero closed (Neumann) eigenvalue of the $p$-Laplacian on compact quaternionic K\"ahler…

The paper is devoted to the study of some properties of the first eigenvalue of the anisotropic $p$-Laplace operator with Robin boundary condition involving a function $\beta$ which in general is not constant. In particular we obtain sharp…

We analyze a general class of difference operators $H_\varepsilon = T_\varepsilon + V_\varepsilon$ on $\ell^2(\varepsilon \mathbb{Z}^d)$, where $V_\varepsilon$ is a one-well potential and $\varepsilon$ is a small parameter. We construct…

If $({\cal E}, {\cal D})$ is a symmetric, regular, strongly local Dirichlet form on $L^2 (X,m)$, admitting a carr\'{e} du champ operator $\Gamma$, and $p>1$ is a real number, then one can define a nonlinear form ${\cal E}^p$ by the formula…

In this paper we discuss applications of the geometric theory of composition operators on Sobolev spaces to the spectral theory of non-linear elliptic operators. The lower estimates of the first non-trivial Neumann eigenvalues of the…

We extend some classical results dealing with boundary Harnack inequatilities to a class of quasilinear elliptic equations and derive some new estimates for solutions of such equations with an isolated singularity on the boundary of a…

We study spectral properties of divergence form elliptic operators $-\textrm{div} [A(z) \nabla f(z)]$ with the Neumann boundary condition in planar domains (including some fractal type domains), that satisfy to the quasihyperbolic boundary…

We consider a classical shape optimization problem for the eigenvalues of elliptic operators with homogeneous boundary conditions on domains in the $N$-dimensional Euclidean space. We survey recent results concerning the analytic dependence…

In this paper we develop numerical analysis for finite element discretization of semilinear elliptic equations with potentially non-Lipschitz nonlinearites. The nonlinearity is essecially assumed to be continuous and monotonically…

The well-known Ambrosetti-Prodi theorem considers perturbations of the Dirichlet Laplacian by a nonlinear function whose derivative jumps over the principal eigenvalue of the operator. Various extensions of this landmark result were…

In this article, we determine the spectrum of real-analytic, non self-adjoint Toeplitz operators on compact K{\"a}hler manifolds and on the complex plane, on neighbourhoods of critical values of the symbol. We consider specifically critical…

We consider a nonlinear elliptic Dirichlet equation driven by a nonlinear nonhomogeneous differential operator involving a Carath\'{e}odory reaction which is $(p-1)$-superlinear but does not satisfy the Ambrosetti-Rabinowitz condition.…

We prove estimates for the variation of the eigenvalues of uniformly elliptic operators with homogeneous Dirichlet or Neumann boundary conditions upon variation of the open set on which an operator is defined. We consider operators of…

We consider a general second-order elliptic differential operator on a domain with a cylindrical end. We impose Dirichlet boundary conditions on the boundary with the exception of a small set, where we impose Neumann boundary conditions.…

We study the inverse problem of determining uniquely and stably quasilinear terms appearing in an elliptic equation from boundary excitations and measurements associated with the solutions of the corresponding equation. More precisely, we…