Author:
Chen Yutong,Su Jiabao,Sun Mingzheng,Tian Rushun
Abstract
In this article we show the existence of nontrivial solutions for nonlocal elliptic equations involving the square root of the Laplacian with the nonlinearity failing to have asymptotic limits at zero and at infinity. We use a combination of homotopy invariance of critical groups and the topological version of linking theorems.
For more information see https://ejde.math.txstate.edu/special/01/c3/abstr.html
Reference47 articles.
1. S. Ahmad, A. C. Lazer, J. L. Paul; Elementary critical point theory and perturbations of elliptic boundary value problems at resonance. Indiana Univ. Math. J., 25 (1976), 933-944.
2. V. Ambrosio, G. M. Bisci, D. Repovs; Nonlinear equations involving the square root of the Laplacian. Discrete Contin. Dyn. Syst. Ser. S, 12 (2019), 151-170.
3. D. Applebaum; Levy processes - from probability to finance and quantum groups. Notices Amer. Math. Soc., 51(2004), 1336-1347.
4. D. Arcoya, E. Colorado, T. Leonori; Asymptotically linear problems and antimaximum principle for the square root of the Laplacian. Advanced Nonlinear Studies, 12 (2012), 683-701.
5. M. Badiale, E. Serra; Semilinear Elliptic Equations for Beginners. Springer, Berlin, 2011.