Multiple solutions of Schrödinger equations with indefinite linear part and super or asymptotically linear terms

Based on new information concerning strongly indefinite functionals without Palais-Smale conditions, we study existence and multiplicity of solutions of the Schrödinger equation

     

Homoclinic orbits for a nonperiodic Hamiltonian system

In this paper we prove the existence and multiplicity of homoclinic orbits for first order Hamiltonian systems of the form

     

Existence and exponential decay of homoclinics in a nonperiodic superquadratic Hamiltonian system

This paper deals with existence and exponential decay of homoclinic orbits in the first-order Hamiltonian system

     

On Hamiltonian elliptic systems with periodic or non-periodic potentials

This paper is concerned with the following Hamiltonian elliptic system

     

Ground state solutions for a periodic Schrödinger equation with superlinear nonlinearities

In this paper we consider the following Schrödinger equation:

     

On the multiplicity of positive solutions for p-Laplace equations via Morse theory

Let us consider the quasilinear problem

     

Existence of homoclinic solutions to periodic orbits in a center manifold

Consider a Lagrangian of the form

     

Nontrivial solutions of some quasilinear problems via a cohomological local splitting

This paper deals with a generalization of the p-Laplacian type boundary value problem

     

Sign-changing saddle point

In this paper, the Saddle-point theorems are generalized to a new version by showing that there exists a “sign-changing” saddle point besides zero. The abstract result is applied to the semilinear elliptic boundary value problem

     

Equivariant bifurcation index

We consider a bifurcation index defined in terms of the degree for G-equivariant gradient maps, see G?ba (1997) [21], Rybicki (1994) [22], Rybicki (2005) [23], where G is a real, compact, connected Lie group and U(G) is the Euler ring of G, see tom Dieck (1977) [29], tom Dieck (1987) [30].The main result of this article is the following:

     

Blowup rate of solutions for a semilinear heat equation with the Neumann boundary condition

Let p>1 and Ω be a smoothly bounded domain in . This paper is concerned with a Cauchy-Neumann problem

     

The minimal period problem for the classical forced pendulum equation

Considered in this paper is the existence/nonexistence of periodic solutions with prescribed minimal periods to the classical forced pendulum equation,

     

Existence and nonexistence of the global solution for the semilinear parabolic system on Riemannian manifold

In this paper, we study the global existence and nonexistence of solutions to the following semilinear parabolic system

     

A sharp form of an embedding into exponential and double exponential spaces

Let Ω be a bounded domain in . In the well-known paper (Indiana Univ. Math. J. 20 (1971) 1077) Moser found the smallest value of K such that