Multiple positive solutions of semilinear elliptic problems in exterior domains.
Multiple positive solutions of singular -Laplacian problems by variational methods.
Multiple radial symmetric solutions for nonlinear boundary value problems of -Laplacian.
Multiple solutions for a class of p(x)-Laplacian equations involving the critical exponent
We study the multiplicity of solutions for a class of p(x)-Laplacian equations involving the critical exponent. Under suitable assumptions, we obtain a sequence of radially symmetric solutions associated with a sequence of positive energies going toward infinity.
Multiple solutions for a problem with resonance involving the -Laplacian.
Multiple solutions for a singular semilinear elliptic problems with critical exponent and symmetries.
Multiple solutions for quasilinear elliptic Neumann problems in Orlicz-Sobolev spaces.
Multiple solutions for singularly perturbed semilinear elliptic equations in bounded domains.
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...