Multiple Solutions for Some Semilinear Elliptic Equations.
Multiple solutions of a nonlinear elliptic equation involving Neumann conditions and a critical Sobolev exponent
Multiple solutions of -Laplacian with Neumann and Robin boundary conditions for both resonance and oscillation problem.
Multiple solutions of supercritical elliptic problems in perturbed domains
Multiple solutions to a singular Lane-Emden-Fowler equation with convection term.
Multiplicative Schwarz Methods for Discontinuous Galerkin Approximations of Elliptic Problems
In this paper we introduce and analyze some non-overlapping multiplicative Schwarz methods for discontinuous Galerkin (DG) approximations of elliptic problems. The construction of the Schwarz preconditioners is presented in a unified framework for a wide class of DG methods. For symmetric DG approximations we provide optimal convergence bounds for the corresponding error propagation operator, and we show that the resulting methods can be accelerated by using suitable Krylov space solvers. A discussion...
Multiplicity bounds for Steklov eigenvalues on Riemannian surfaces
We prove two explicit bounds for the multiplicities of Steklov eigenvalues on compact surfaces with boundary. One of the bounds depends only on the genus of a surface and the index of an eigenvalue, while the other depends as well on the number of boundary components. We also show that on any given Riemannian surface with smooth boundary the multiplicities of Steklov eigenvalues are uniformly bounded in .
Multiplicity of nontrivial solutions for Kirchhoff type problems.
Multiplicity of positive and nodal solutions for nonhomogeneous elliptic problems in unbounded cylinder domains.
Multiplicity of solutions for a singular p-laplacian elliptic equation
The existence of two continuous solutions for a nonlinear singular elliptic equation with natural growth in the gradient is proved for the Dirichlet problem in the unit ball centered at the origin. The first continuous solution is positive and maximal; it is obtained via the regularization method. The second continuous solution is zero at the origin, and follows by considering the corresponding radial ODE and by sub-sup solutions method.
Multiplicity of solutions of nonlinear boundary value problems with nonlinearities crossing several higher eigenvalues.
Multiplicity results for a family of semilinear elliptic problems under local superlinearity and sublinearity
We study the existence, nonexistence and multiplicity of positive solutions for the family of problems , , where is a bounded domain in , and is a parameter. The results include the well-known nonlinearities of the Ambrosetti–Brezis–Cerami type in a more general form, namely , where . The coefficient is assumed to be nonnegative but is allowed to change sign, even in the critical case. The notions of local superlinearity and local sublinearity introduced in [9] are essential in this...
Multiplicity results for a perturbed elliptic Neumann problem.
Multiplicity results for nonlinear elliptic equations.
Multiplicity results for -Laplacian with critical nonlinearity of concave-convex type and sign-changing weight functions.
Multiplicity results of positive radial solutions for -Laplacian problems in exterior domains.
Multipliers in Sobolev spaces and exact convergence rate estimates for the finite-difference schemes
In this paper we present some recent results concerning convergence rate estimates for finite-difference schemes approximating boundary-value problems. Special attention is given to the problem of minimal smoothness of coefficients in partial differential equations necessary for obtaining the results.
Multiscale expansion and numerical approximation for surface defects⋆
This paper is a survey of articles [5, 6, 8, 9, 13, 17, 18]. We are interested in the influence of small geometrical perturbations on the solution of elliptic problems. The cases of a single inclusion or several well-separated inclusions have been deeply studied. We recall here techniques to construct an asymptotic expansion. Then we consider moderately close inclusions, i.e. the distance between the inclusions tends to zero more slowly than their characteristic size. We provide a complete asymptotic...