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- W2617246475 abstract "This paper establishes sufficient conditions for the existence and multiplicity of solutions for nonhomogeneous and singular quasilinear equations of the form − Δ u + V ( x ) u − Δ ( u 2 ) u = g ( x , u ) | x | a + h ( x ) in R 2 , where a ∈ [ 0 , 2 ) , V ( x ) is a continuous positive potential bounded away from zero and which can be “large” at infinity, the nonlinearity g ( x , s ) is allowed to enjoy the critical exponential growth with respect to the Trudinger–Moser inequality and the nonhomogeneous term h belongs to L q ( R 2 ) for some q ∈ ( 1 , 2 ] . By combining variational arguments in a nonstandard Orlicz space context with a singular version of the Trudinger–Moser inequality, we obtain the existence of two distinct solutions when ‖ h ‖ q is sufficiently small. Schrödinger equations of this type have been studied as models of several physical phenomena." @default.
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- W2617246475 date "2017-08-01" @default.
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- W2617246475 title "On a nonhomogeneous and singular quasilinear equation involving critical growth in<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=mml1 display=inline overflow=scroll altimg=si1.gif><mml:msup><mml:mrow><mml:mi mathvariant=double-struck>R</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:math>" @default.
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- W2617246475 doi "https://doi.org/10.1016/j.camwa.2017.05.002" @default.
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