Landesman–Lazer Type Conditions and Multiplicity Results for Nonlinear Elliptic Problems with Neumann Boundary Values
Landesman–Lazer Type Conditions and Multiplicity Results for Nonlinear Elliptic Problems with Neumann Boundary Values
摘要
We establish the existence and multiplicity of solutions for Steklov problems under non- resonance or resonance conditions using variational methods. In our main theorems, we consider a weighted eigenvalue problem of Steklov type.
We establish the existence and multiplicity of solutions for Steklov problems under non- resonance or resonance conditions using variational methods. In our main theorems, we consider a weighted eigenvalue problem of Steklov type.
基金
partially supported by CNPq-Procad
参考文献21
-
1Ambrossetti, A., Mancini, G.: Existence and multiplicity results for nonlinear elliptic problems with linear part at resonance. The case of the simple eigenvalue. J. Differ. Equ., 28, 220-245 (1978).
-
2Ambrossetti, A., Mancini, G.: Theorems of existence and multiplicity for nonlinear elliptic problem with noninvertible linear part. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 5, 15-28 (1978).
-
3Bonder, J. F.: Multiply solutions for the p-Laplacian equation with nolinear boundary conditions. Electron. J. Diff. Equ., 37, 1-7 (2007).
-
4Bundle, C.: Isoperimetric Inequalities and Applications, Pitman Publishing, Boston, 1980.
-
5Chang, K. C.: Morse theory and multiple solution problems. Progress in Nonlinear Differential Equations and their Applications, 6, Birkhauser, Boston, 1993.
-
6de Figueiredo, D. G.: Positive Solutions of Semilinear Elliptic Problems, Lectures in Notes in Math., 957, 34-87 (1982).
-
7Escobar, J. F.: A comparison theorem for the first non-zero Steklov eigenvalue. J. Func. Anal., 178, 143-155 (2001).
-
8Escobar, J. F.: Conformal metrics with prescribed mean curvature on the boundary. Calc. Var., 4, 559-592 (1996).
-
9Giovanni, C.: A Landesman-Lazer type condition for a nonlinear Steklov Problem. NoDEA Nonlinear Differential Equations Appl., 14, 729-738 (2007).
-
10Landesman, E. M., Lazer, A. C.: Nonlinear pertubations of linear eigevalues problem at resonance. J. Math. Mech., 19, 609-623 (1970).
-
1黄毅生,虚成林.拟线性方程解的存在性(英文)[J].应用泛函分析学报,2003,5(4):311-318.
-
2王雄瑞.半线性椭圆型方程解的存在性[J].宜宾学院学报,2009,9(12):5-8. 被引量：1
-
3Aixia QIAN.Sign-Changing Solutions for a Class of Nonlinear Elliptic Problems[J].Chinese Annals of Mathematics,Series B,2007,28(5):609-616.
-
4张祥.BOUNDARY AND INTERIOR LAYER PHENOMENA OF SINGULARLY PERTURBED NONLINEAR ELLIPTIC PROBLEMS[J].Acta Mathematica Scientia,1999,19(S1):589-597.
-
5张岩文,张建军.N_2分子电子振动光谱德兰德斯表的绘制及其分析[J].石河子大学学报（自然科学版）,2010,28(1):128-132.
-
6朱宝骧,郭金勇.粘性p-双调和抛物型方程弱解的唯一性[J].柳州师专学报,2014,29(5):145-147.
-
7SHEN Chun-fang,YANG Liu,LIU Xi-ping.Multiplicity Results for Second-order Generalized Sturm-Liouville Boundary Value Problems with Dependence on the First Order Derivative[J].Chinese Quarterly Journal of Mathematics,2007,22(1):114-125. 被引量：1
-
8SHEN ZhongMin,XIA QiaoLing.On conformal vector fields on Randers manifolds[J].Science China Mathematics,2012,55(9):1869-1882. 被引量：6
-
9谢资清.MULTIPLICITY RESULTS FOR AN INHOMOGENEOUS NONLINEAR ELLIPTIC PROBLEM[J].Acta Mathematica Scientia,1999,19(2):158-167. 被引量：1
-
10ZHOU Zhan,MA DeFang.Multiplicity results of breathers for the discrete nonlinear Schrodinger equations with unbounded potentials[J].Science China Mathematics,2015,58(4):781-790. 被引量：1
