Heteroclinic solutions for the extended Fisher–Kolmogorov equation

On the Solution of a Nonhomogeneous Fisher-Kolmogorov Equation

“…In (Andreu, Caselles & Maz´on, 2010), a Fisher-Kolmogorov type equation is taken into account and it is proved that the existence and uniqueness of finite speed moving fronts and the existence of some explicit solutions in a particular regime of the equation. In (Yeun, 2013), it is studied the extended Fisher-Kolmogorov (EFK) equation and its variants. In (Danumjaya & Pani, 2005), a second-order splitting combined with orthogonal cubic spline collocation method is formulated and analysed for the extended Fisher-Kolmogorov equation.…”

Infinitely Many Homoclinic Solutions for Fourth Order p-Laplacian Differential Equations

“…They are known in phase transitions models as ground states or pulses (see [1]). The existence of homoclinic and heteroclinic solutions of fourth-order equations is studied by various authors (see [2][3][4][5][6][7][8][9][10][11][12] and references therein). Sun and Wu [4] obtained existence of two homoclinic solutions for a class of fourth-order differential equations:…”

Multiplicity of Homoclinic Solutions for a Class of Nonperiodic Fourth-Order Differential Equations with General Perturbation

“…Recently, a lot of attention has been focused on the study of homoclinic and heteroclinic solutions for this problem; see [1][2][3][4][5][6][7][8]. This may be due to its concrete applications, such as physics and mechanics; see [9,10].…”