# A local mountain pass type result for a system of nonlinear Schrï¿½dinger equations

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The purpose of this paper is to investigate the existence of solutions to the following quasilinear SchrÃ¶dinger type system driven by the fractional p-Laplacian (-Î”)psu + a(x)|u|p-2u = Hu(x, u, v) in RN, (-Î”)qsv + b(x)|v|q-2v = Hv(x, u, v) in RN, where 1 < q â‰¤ p, sp < N,...

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This paper is concerned with the existence of positive solutions for a class of quasilinear SchrÃ¶dinger equations in âƒ¿N with critical growth and potential vanishing at infinity. By using a change of variables, the quasilinear equations are reduced to semilinear one. Since the potential...

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We prove the existence of infinitely many radially symmetric standing-wave solutions of the Chern-Simons-SchrÃ¶dinger system. Our result is established by applying the mountain-pass theorem to the functional, which is obtained by representing gauge fields AÎ¼ in terms of a scalar field...

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It is established the existence of solutions for a class of asymptotically periodic quasilinear elliptic equations in $${\mathbb{R}^N}$$ with critical growth. Applying a change of variable, the quasilinear equations are reduced to semilinear equations, whose respective associated functionals are...

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In the present paper we study the existence of solutions for a nonlocal SchrÃ¶dinger equation --ÎµÂ² Î”u + V (x)u = (Î”â„Â³ |u|p/|x - y|Âµ dy)|u|p-2u, where 0 < Âµ < 3 and 6-Âµ/3 < p < 6 - Âµ. Under suitable assumptions on the potential V (x), if the parameter Îµ is...

- ON THE MOUNTAIN-PASS ALGORITHM FOR THE QUASI-LINEAR SCHRÃ–DINGER EQUATION. GRUMIAU, CHRISTOPHER; SQUASSINA, MARCO; TROESTLER, CHRISTOPHE // Discrete & Continuous Dynamical Systems - Series B;Jul2013, Vol. 18 Issue 5, p1345
We discuss the application of the Mountain Pass Algorithm to the so-called quasi-linear SchrÃ¶dinger equation, which is naturally associated with a class of nonsmooth functionals so that the classical algorithm cannot directly be used. A change of variable allows us to deal with the lack of...