Triple variational principles for self-adjoint operator functions

Triple variational principles for self-adjoint operator functions

Article history: Received 13 June 2013 Accepted 3 September 2015 Available online 19 January 2016 Communicated by L. Gross MSC: primary 49R05 secondary 47A56, 47A10

The Laplace operator is essentially self-adjoint

Correspondence of the eigenvalues of a non-self-adjoint operator to those of a self-adjoint operator

We prove that the eigenvalues of a certain highly non-self-adjoint operator that arises in fluid mechanics correspond, up to scaling by a positive constant, to those of a self-adjoint operator with compact resolvent; hence there are infinitely many real eigenvalues which accumulate only at ±∞. We use this result to determine the asymptotic distribution of the eigenvalues and to compute some of ...

Index theory for linear self-adjoint operator equations and nontrivial solutions for asymptotically linear operator equations

We will first establish an index theory for linear self-adjoint operator equations. And then with the help of this index theory we will discuss existence and multiplicity of solutions for asymptotically linear operator equations by making use of the dual variational methods and Morse theory. Finally, some interesting examples concerning second order Hamiltonian systems, first order Hamiltonian ...

Bernstein Widths of Some Classes of Functions Defined by a Self-Adjoint Operator

Guo Feng School of Mathematics and Information Engineering, Taizhou University, Taizhou 317000, China Correspondence should be addressed to Guo Feng, [email protected] Received 9 May 2011; Accepted 2 August 2011 Academic Editor: Kai Diethelm Copyright q 2012 Guo Feng. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distri...