Sequences of positive homoclinic solutions to difference equations with variable exponent

Homoclinic Solutions for a Class of Nonlinear Difference Equations

Anisotropic quasilinear elliptic equations with variable exponent

We study some anisotropic boundary value problems involving variable exponent growth conditions and we establish the existence and multiplicity of weak solutions by using as main argument critical point theory. 2000 Mathematics Subject Classification: 35J60, 35J62, 35J70.

EXISTENCE OF HOMOCLINIC SOLUTIONS FOR SECOND ORDER DIFFERENCE EQUATIONS WITH p-LAPLACIAN

Using the variational method and critical point theory, the authors study the existence of infinitely many homoclinic solutions to the difference equation −∆ ( a(k)φp(∆u(k − 1)) ) + b(k)φp(u(k)) = λf(k, u(k))), k ∈ Z, where p > 1 is a real number, φp(t) = |t|p−2t for t ∈ R, λ > 0 is a parameter, a, b : Z→ (0,∞), and f : Z × R → R is continuous in the second variable. Related results in the lite...

Infinitely Many Homoclinic Solutions for Second Order Nonlinear Difference Equations with p-Laplacian

We employ Nehari manifold methods and critical point theory to study the existence of nontrivial homoclinic solutions of discrete p-Laplacian equations with a coercive weight function and superlinear nonlinearity. Without assuming the classical Ambrosetti-Rabinowitz condition and without any periodicity assumptions, we prove the existence and multiplicity results of the equations.

Rational expansion method of exponent function for solving exact solutions to nonlinear differential-difference equations

A new method named rational expansion method of exponent function is presented to find exact traveling wave solutions of differential-difference equations. This method generalizes the so-called tanh-method and other similar methods. Some examples are dealt with and their abundant exact solutions which include solitary solutions and periodic solutions are obtained. Among them, many solutions are...