Normalized solutions for the double-phase problem with nonlocal reaction

Abstract

In this article, we consider the double-phase problem with nonlocal reaction. For the autonomous case, we introduce the methods of the Pohozaev manifold, Hardy-Littlewood Sobolev subcritical approximation, adding the mass term to prove the existence and nonexistence of normalized solutions to this problem. For the nonautonomous case, we show the existence of normalized solutions to the double-phase problem by using the Pohozaev restrict method and describing the relationship between the energy of this problem and its limit problem. Moreover, we study the existence of normalized solutions to the double-phase problem involving double Hardy-Littlewood-Sobolev critical exponents.

Keywords

• double-phase problem
• normalized solutions
• hardy-littlewood-sobolev critical exponent
• 35a15
• 35b09
• 35j92