Multiple solutions with compact support for a quasilinear Schrödinger equation with sign-changing potentials

References

• Bedoui N, Ounaies H. Qualitative properties and support compactness of solutions for quasilinear Schrödinger equation with sign changing potentials. Nonlinear Anal. 2020;198:111843.
   Google Scholar
• Díaz JI. Nonlinear partial differential equations and free boundaries, volume I, elliptic equations. Pitman; 1985. (Research Notes in Mathematics; 106).
   Google Scholar
• Fife PC. Asymptotic states for equations of reaction and diffusion. Bull Amer Math Soc. 1978;84:693–727.
   Web of Science ®Google Scholar
• Ambrosetti A, Rabinowitz PH. Dual variational methods in critical point theory and applications. J Funct Anal. 1973;14:349–381.
   Google Scholar
• Bahrouni A, Ounaies H, Rădulescu V. Infinitely many solutions for a class of sublinear Schrödinger equations with sign-changing potentials. Proc Royal Soc Edinburgh Sect A. 2015;145:445–465.
   Web of Science ®Google Scholar
• Bahrouni A, Ounaies H, Rădulescu V. Bound state solutions of sublinear Schrödinger equations with lack of compactness. submitted.
   Google Scholar
• Chabrowski J, Costa DG. On a class of Schrödinger-type equations with indefinite weight functions. Commun Partial Differ Equ. 2008;33:1368–1394.
   Web of Science ®Google Scholar
• Kajikiya R. A critical point theorem related to the symmetric mountain pass lemma and its applications to elliptic equations. J Funct Anal. 2005;225:352–370.
   Web of Science ®Google Scholar
• Tehrani H. Existence results for an indefinite unbounded perturbation of a resonant Schrödinger equation. J Differ Equ. 2007;236:1–28.
   Web of Science ®Google Scholar
• Su J, Wang Z, Willem M. Weighted Sobolev embedding with unbounded and decaying radial potentials. J Differ Equ. 2007;238:201–219.
   Web of Science ®Google Scholar
• Alama S, Lu Q. Compactly supported solutions to stationary degenerate diffusion equations. J Differ Equ. 2009;246:3214–3240.
   Web of Science ®Google Scholar
• Bahrouni A, Ounaies H, Rădulescu V. Compactly supported solutions of Schrödinger equations with small perturbation. App Math Lett. 2018;84:148–154.
   Web of Science ®Google Scholar
• Bégout P, Díaz JI. On a nonlinear Schrödinger equation with a localizing effect. CR Acad Sci Paris, Sér I. 2006;342:459–463.
   Google Scholar
• Bégout P, Díaz JI. Localizing estimates of the support of solutions of some nonlinear Schrödinger equations: the stationary case. Ann Inst H Poincaré, Anal Non Linéaire. 2012;29:35–58.
   Web of Science ®Google Scholar
• Bégout P, Díaz JI. Self-similar solutions with compactly supported profile of some nonlinear Schrödinger equations. Electronic J Differ Equ. 2014;2014:1–15.
   Google Scholar
• Bégout P, Díaz JI. A sharper energy method for the localization of the support to some stationary Schrödinger equations with a singular nonlinearity. Discrete Continuous Dyn Syst. 2014;34:3371–3382.
   Web of Science ®Google Scholar
• Bégout P, Díaz JI. Existence of weak solutions to some stationary Schrödinger equations with singular nonlinearity. Rev R Acad Cien Serie A Mat (RACSAM). 2015;109(1):43–63.
   Google Scholar
• Cortazar C, Elgueta M, Felmer P. On a semilinear elliptic problem in RN with a non-lipschitzian nonlinearity. Adv Differ Equ. 1996;1:199–218.
   Google Scholar
• Díaz JI. On the ambiguous treatment of the Schrödinger equation for the infinite potential well and an alternative via flat solutions: the one-dimensional case. Interfaces and Free Boundaries. 2015;17:333–351.
   Web of Science ®Google Scholar
• Díaz JI. On the ambiguous treatment of the Schrödinger equation for the infinite potential well and an alternative via singular potentials: the multi-dimensional case. SeMA-J. DOI:https://doi.org/10.1007/s40324-017-0115-3. Published online 6 March 2017
   Google Scholar
• Lu Q. Compactly supported solutions for a semilinear elliptic problem in Rn with sign-changing function and non-Lipschitz nonlinearity. Proceedings of the Royal Society of Edinburgh. 2011;141:127–154.
   Google Scholar
• Lu Q. Multiple solutions with compact support for a semilinear elliptic problem with critical growth. J Differ Equ. 2012;252:6275–6305.
   Web of Science ®Google Scholar
• Cortazar C, Dolbeault J, Huidobro M, et al. Existence of sign changing solutions for an equation with a weighted p-Laplace operator. Nonlinear Anal. 2014;110:1–22.
   Web of Science ®Google Scholar
• Dolbeault J, Garcia-Huidobro M, Manasevich R. Qualitative properties and existence of sign changing solutions with compact support for an equation with a p-Laplace operator. Adv Nonlinear Stud. 2013;13:149–178.
   Web of Science ®Google Scholar