Electronic Journal of Differential Equations
https://digital.library.txstate.edu/handle/10877/86
2020-05-30T00:21:40ZNontrivial Periodic Solutions of Asymptotically Linear Hamiltonian Systems
https://digital.library.txstate.edu/handle/10877/9330
Nontrivial Periodic Solutions of Asymptotically Linear Hamiltonian Systems
Fei, Guihua
We study the existence of periodic solutions for some asymptotically linear Hamiltonian systems. By using the Saddle Point Theorem and Conley index theory, we obtain new results under asymptotically linear conditions.
2001-11-19T00:00:00ZStability Properties of Positive Solutions to Partial Differential Equations with Delay
https://digital.library.txstate.edu/handle/10877/9329
Stability Properties of Positive Solutions to Partial Differential Equations with Delay
Farkas, Gyula; Simon, Peter L
We investigate the stability of positive stationary solutions of semilinear initial-boundary value problems with delay and convex or concave nonlinearity. If the nonlinearity is monotone, then in the convex case <i>f</i>(0) ≤ 0 implies instability and in the concave case <i>f</i>(0) ≥ 0 implies stability. Special cases are shown where the monotonicity assumption can be weakened or omitted.
2001-10-08T00:00:00ZGlobal Bifurcation Result for the p-Biharmonic Operator
https://digital.library.txstate.edu/handle/10877/9328
Global Bifurcation Result for the p-Biharmonic Operator
Drabek, Pavel; Otani, Mitsuharu
We prove that the nonlinear eigenvalue problem for the p-biharmonic operator with p > 1, and Ω a bounded domain in ℝN with smooth boundary, has principal positive eigenvalue λ1 which is simple and isolated. The corresponding eigenfunction is positive in Ω and satisfies ∂u/∂n < 0 on ∂Ω, ∆u1 < 0 in Ω. We also prove that (λ1, 0) is the point of global bifurcation for associated nonhomogeneous problem. In the case <i>N</i> = 1 we give a description of all eigenvalues and associated eigenfunctions. Every such an eigenvalue is then the point of global bifurcation.
2001-07-03T00:00:00ZAsymptotic Behavior of Solutions to Wave Equations with a Memory Condition at the Boundary
https://digital.library.txstate.edu/handle/10877/9327
Asymptotic Behavior of Solutions to Wave Equations with a Memory Condition at the Boundary
Santos, Mauro de Lima
In this paper, we study the stability of solutions for wave equations whose boundary condition includes a integral that represents the memory effect. We show that the dissipation is strong enough to produce exponential decay of the solution, provided the relaxation function also decays exponentially. When the relaxation function decays polynomially, we show that the solution decays polynomially and with the same rate.
2001-11-26T00:00:00Z