Existence of positive solutions for boundary value problems of second-order nonlinear differential equations on the half line.
Existence of quasilinear relaxation shock profiles in systems with characteristic velocities
We revisit the existence problem for shock profiles in quasilinear relaxation systems in the case that the velocity is a characteristic mode, implying that the profile ODE is degenerate. Our result states existence, with sharp rates of decay and distance from the Chapman–Enskog approximation, of small-amplitude quasilinear relaxation shocks. Our method of analysis follows the general approach used by Métivier and Zumbrun in the semilinear case, based on Chapman–Enskog expansion and the macro–micro...
Existence of solutions for second-order differential equations and systems on infinite intervals.
Existence of solutions to second order ordinary differential equations having finite limits at infinity.
Existence of three positive solutions for -point discrete boundary value problems with -Laplacian.
Existence problems for homoclinic solutions.
Existence problems for -closed orbits.
Fast and heteroclinic solutions for a second order ODE.
Heteroclinic orbits in plane dynamical systems
We consider general second order boundary value problems on the whole line of the type , , for which we provide existence, non-existence, multiplicity results. The solutions we find can be reviewed as heteroclinic orbits in the plane dynamical system.
Heteroclinic solutions to an asymptotically autonomous second-order equation.
Homoclinic solutions for linear and linearizable ordinary differential equations.
Homoclinic solutions of singular nonautonomous second-order differential equations.
Limits of solutions of a perturbed linear differential equation.
Localized radial solutions for a nonlinear -Laplacian equation in .
Multiple positive solutions for a second order delay boundary value problem on the half-line
Second order nonlinear delay differential equations are considered, and Krasnosel'skiĭ's fixed point theorem is used to establish a result on the existence of positive solutions of a boundary value problem on the half-line. This result can be used to guarantee the existence of multiple positive solutions. A specification of the result obtained to the case of second order nonlinear ordinary differential equations as well as to a particular case of second order nonlinear delay differential equations...
Multiple positive solutions for boundary value problems of second-order differential equations system on the half-line.
Multiple positive solutions for singular boundary-value problems with derivative dependence on finite and infinite intervals.
New exact traveling wave solutions of the ()-dimensional Zakharov-Kuznetsov (ZK) equation.
On a boundary value problem with a weighted condition at infinity for even-order nonlinear ordinary differential equations.
On a singular multi-point third-order boundary value problem on the half-line
We establish not only sufficient but also necessary conditions for existence of solutions to a singular multi-point third-order boundary value problem posed on the half-line. Our existence results are based on the Krasnosel’skii fixed point theorem on cone compression and expansion. Nonexistence results are proved under suitable a priori estimates. The nonlinearity which satisfies upper and lower-homogeneity conditions in the space variables may be also singular at time . Two examples of applications...