By means of variational methods we prove the existence of a positive, homoclinic solution to an equation of the kind u''=au-bu^p, where p>1, and both coefficients a(x), b(x) are positive and asymptotically constant. Our main result requires a control from above on the ratios .between the supremum of a(x) and its limit at infinity and between the limit at infinity of b(x) and its infimum.
Positive homoclinic solutions to some Schrodinger type equations / Gavioli, Andrea; Sanchez, Luis. - In: DIFFERENTIAL AND INTEGRAL EQUATIONS. - ISSN 0893-4983. - 7-8:(2016), pp. 665-682.
Positive homoclinic solutions to some Schrodinger type equations
GAVIOLI, Andrea;
2016
Abstract
By means of variational methods we prove the existence of a positive, homoclinic solution to an equation of the kind u''=au-bu^p, where p>1, and both coefficients a(x), b(x) are positive and asymptotically constant. Our main result requires a control from above on the ratios .between the supremum of a(x) and its limit at infinity and between the limit at infinity of b(x) and its infimum.
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