Related papers: Quasilinear eigenvalues

We consider singular solutions to quasilinear elliptic equations under zero Dirichlet boundary condition. Under suitable assumptions on the nonlinearity we deduce symmetry and monotonicity properties of positive solutions via an improved…

The Jacobian elliptic functions are generalized and applied to a nonlinear eigenvalue problem with $p$-Laplacian. The eigenvalue and the corresponding eigenfunction are represented in terms of common parameters, and a complete description…

We investigate the monotonicity of the minimal period of periodic solutions of quasilinear differential equations involving the $p$-Laplace operator. First, the monotonicity of the period is obtained as a function of a Hamiltonian energy in…

A new idea to approximate the second eigenfunction and the second eigenvalue of $p$-Laplace operator is given. In the case of the Dirichlet boundary condition, the scheme has the restriction that the positive and the negative part of the…

In this paper, we establish several inequalities of Dirichlet eigenvalues for Laplace operator $\Delta $ with any order on \emph{n}-dimensional Euclidean space. These inequalities are more general than known Yang's inequalities and contain…

We are mainly concerned with equations of the form $-Lu=f(x,u)+\mu$, where $L$ is an operator associated with a quasi-regular possibly nonsymmetric Dirichlet form, $f$ satisfies the monotonicity condition and mild integrability conditions,…

In this work we consider a system of quasilinear elliptic equations driven by an anisotropic $p$-Laplacian. The lower-order nonlinearities are in potential form and exhibit critical Sobolev growth. We exhibit conditions on the coefficients…

We study spectral estimates of the divergence form uniform elliptic operators $-\textrm{div}[A(z) \nabla f(z)]$ with the Dirichlet boundary condition in bounded non-Lipschitz simply connected domains $\Omega \subset \mathbb C$. The…

We introduce a new class of quasilinear nonlocal operators and study equations involving these operators. The operators are degenerate elliptic and may have arbitrary growth in the gradient. Included are new nonlocal versions of p-Laplace,…

We deal with the sharp asymptotic behaviour of eigenvalues of elliptic operators with varying mixed Dirichlet-Neumann boundary conditions. In case of simple eigenvalues, we compute explicitly the constant appearing in front of the…

We consider a family of quasilinear second order elliptic differential operators which are not coercive and are defined by functions in Marcinkiewicz spaces. We prove the existence of a solution to the corresponding Dirichlet problem. The…

We study existence of solutions for a boundary degenerate (or singular) quasilinear equation in a smooth bounded domain under Dirichlet boundary conditions. We consider a weighted $p-${L}aplacian operator with a coefficient that is {locally…

In this article we prove some Lipschitz estimates and existence result for a class of degenerate fully nonlinear elliptic equations which are a generalization of the pseudo p-Laplacian. The operators are degenerate elliptic at any point…

Let $\Omega$ be a bounded open set of $\mathbb R^{n}$, $n\ge 2$. In this paper we mainly study some properties of the second Dirichlet eigenvalue $\lambda_{2}(p,\Omega)$ of the anisotropic $p$-Laplacian \[ -\mathcal Q_{p}u:=-\textrm{div}…

we introduce a generalization of the $p$-Laplace operator to act on differential forms and generalize an estimate of Gallot-Meyer for the first nonzero eigenvalue on closed Riemannian manifolds.

This paper is concerned with spectral estimates for the first Dirichlet eigenvalue of the degenerate $p$-Laplace operator in bounded simply connected domains $\Omega \subset \mathbb C$. The proposed approach relies on the conformal analysis…

We establish gradient H\"older continuity for solutions to quasilinear, uniformly elliptic equations, including $p$-Laplace and Orlicz-Laplace type operators. We revisit and improve upon the results existing in the literature, proving…

We study a system of quasilinear eigenvalue problems with Dirichlet boundary conditions on complete compact Riemannian manifolds. In particular, Cheng comparison estimates and inequality of Faber-Krahn for the first eigenvalue of a…

In this paper, we obtain a new abstract formula relating eigenvalues of a self-adjoint operator to two families of symmetric and skew-symmetric operators and their commutators. This formula generalizes earlier ones obtained by Harrell,…

We consider second order uniformly elliptic operators of divergence form in $\R^{d+1}$ whose coefficients are independent of one variable. For such a class of operators we establish a factorization into a product of first order operators…