TY - JOUR
ID - 12997
TI - On the existence of solutions to a class of semilinear Schrödinger equations
JO - Journal of Advanced Mathematical Modeling
JA - JAMM
LA - en
SN - 2251-8088
AU - Jalilian, Yaghoob
AU - Dehsari, Iraj
AD - Department of Mathematics, Razi University, Kermanshah, Iran
Y1 - 2017
PY - 2017
VL - 6
IS - 2
SP - 75
EP - 91
KW - Quasilinear Schrödinger equation
KW - Natural constraint
KW - Nehari manifold
KW - Weak solution
KW - Existence of solution
DO - 10.22055/jamm.2017.12997
N2 - In this paper, we investigate the existence of a nontrivial weak solution for a class of quasilinear Schrödinger equations in the Sobolev space . First, we use a change of variables to obtain a well defined energy functional on . Then we find a manifold which is a natural constraint, and we prove that the restriction of the energy functional to this manifold attains its infimum. Finally, we show that this infimum point is a nontrivial weak solution for the equation.
UR - https://jamm.scu.ac.ir/article_12997.html
L1 - https://jamm.scu.ac.ir/article_12997_d4ab42cd3fe23af00e7154d1808d72d0.pdf
ER -