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- W2893624684 abstract "The multiplicity of solutions for a $(p,q)$ -Laplacian equation involving critical exponent $$ -Delta_{p}u-Delta_{q}u=lambda V(x) vert u vert ^{k-2}u+K(x) vert u vert ^{p^{ast }-2}u,quad xin mathbb{R}^{N} $$ is considered. By variational methods and the concentration–compactness principle, we prove that the problem possesses infinitely many weak solutions with negative energy for $lambdain(0,lambda^{ast})$ . Moreover, the existence of infinitely many solutions with positive energy is also given for all $lambda>0$ under suitable conditions." @default.
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- W2893624684 date "2018-09-25" @default.
- W2893624684 modified "2023-09-26" @default.
- W2893624684 title "Multiplicity of solutions for a quasilinear elliptic equation with ( p , q ) $(p,q)$ -Laplacian and critical exponent on R N $mathbb{R}^{N}$" @default.
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- W2893624684 doi "https://doi.org/10.1186/s13661-018-1068-x" @default.
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