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| Paper IPM / M / 16302 |
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| Abstract: | |
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This paper focuses on the scalar field equation D^2α_x uâνuâu_yy=f(u), where αâ(0,1), (x,y)âR^NÃ(âL,L)âR^N+1, with Nâ¥1 and D^2α_ x stands for the fractional Laplacian. By using several variational methods, we establish the existence, long behavior, and multiplicity of solutions of this equation under the Dirichlet and Neumann boundary conditions.
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