Homoclinic solutions for ordinary image-Laplacian systems with a coercive potential Original Research Article

A result for the existence of homoclinic orbits is obtained for pp-Laplacian systems View the MathML sourceddt(|u̇(t)|p−2u̇(t))=∇F(t,u(t))+f(t), where p>1,u∈Rnp>1,u∈Rn, F∈C1(R×Rn,R)F∈C1(R×Rn,R) is TT-periodic with respect to tt and f:R→Rnf:R→Rn is a continuous and bounded function such that F(t,x)≥F(t,0)+b|x|μF(t,x)≥F(t,0)+b|x|μ and View the MathML source∫R|f(t)|μ/(μ−1)dt<∞ for some b>0b>0 and μ>1μ>1.