EXISTENCE OF SOLUTION FOR A CLASS OF INDEFINITE VARIATIONAL PROBLEMS WITH DISCONTINUOUS NONLINEARITY

被引：3
作者：
Alves C.O. [1 ]
Patricio G.F. [1 ]
机构：
[1] Universidade Federal de Campina Grande, Unidade Acadêmica de Matemática - UAMat, PB, Campina Grande
来源：
Journal of Mathematical Sciences | 2022年 / 266卷 / 4期
关键词：
Discontinuous nonlinearity; Elliptic problem; Variational methods;
D O I：
10.1007/s10958-022-05991-w
中图分类号：
学科分类号：
摘要：
This paper concerns the existence of a nontrivial solution for the following problem(P){-Δu+V(x)u∈∂uF(x,u)a.e. inRN,u∈H1(RN). where F(x,t)=∫0tf(x,s)ds, f is a ZN-periodic measurable function and λ = 0 does not belong to the spectrum of −Δ + V. Here, ∂tF denotes the generalized gradient of F with respect to variable t. © 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.
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页码：635 / 663
页数：28
相关论文
共 56 条
[1]  
Alama S., Li Y.Y., On ”multibump” bound states for certain semilinear elliptic equations, Indiana Univ. Math. J., 41, pp. 983-1026, (1992)
[2]  
Angenent S., The shadowing lemma for elliptic PDE, in: Dynamics of Infinite-Dimensional Systems, Lisbon, 1986, 37, pp. 7-22, (1987)
[3]  
Coti Zelati V., P.H. Rabinowitz Homoclinic type solutions for a semilinear elliptic PDE on RN, Comm. Pure Appl. Math, 45, pp. 1217-1269, (1992)
[4]  
Kryszewski W., Szulkin A., (1998)
[5]  
Arioli G., Szulkin A., A Semilinear Schrödinger Equation in the Presence of a Magnetic Field, Arch. Rational Mech. Anal., 170, (2003)
[6]  
Barstch T., Ding Y.
[7]  
Chabrowski J., Szulkin A., On a semilinear Schrödinger equation with critical Sobolev exponent, Proc. Amer. Math. Soc., 130, pp. 85-93, (2001)
[8]  
Szulkin A., Zou W., Homoclinic orbits for asymptotically linear Hamiltonian systems, J. Funct. Anal., 187, pp. 25-41, (2001)
[9]  
Schechter M., Zou W., Weak linking theorems and Schrödinger equations with critical sobolev exponent, ESAIM: COCV, 9, pp. 601-619, (2003)
[10]  
Ackermann N., On a periodic Schrödinger equation with nonlocal superlinear part, Mathematische Zeitschrift, 248, 2, (2004)
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