On the Schrödinger equation involving a critical Sobolev exponent and magnetic field
Keywords
Semilinear Schrödinger equation, critical Sobolev exponent, magnetic field, linkingAbstract
We consider the semilinear Schrödinger equation $$ -\Delta_A u+V(x)u =Q(x)|u|^{2^{*}-2}u. $$ Assuming that $V$ changes sign, we establish the existence of a solution $u\ne 0$ in the Sobolev space $ H_{A,V^+}^{1}(\RN)$. The solution is obtained by a min-max type argument based on a topological linking. We also establish certain regularity properties of solutions for a rather general class of equations involving the operator $-\Delta_A$.Downloads
Published
2005-03-01
How to Cite
1.
CHABROWSKI, Jan and SZULKIN, Andrzej. On the Schrödinger equation involving a critical Sobolev exponent and magnetic field. Topological Methods in Nonlinear Analysis. Online. 1 March 2005. Vol. 25, no. 1, pp. 3 - 21. [Accessed 28 March 2024].
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