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Alexandru Kristá ly Csaba Varga 《Proceedings of the American Mathematical Society》2007,135(7):2121-2126
For certain positive numbers and we establish the multiplicity of solutions to the problem where is a bounded open domain in containing the origin with smooth boundary while is continuous, superlinear at zero and sublinear at infinity.
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OSCILLATION OF CERTAIN SECOND ORDER DIFFERENCE EQUATIONS 总被引:4,自引:0,他引:4
1IntroductionConsiderasec0nd0rderdifferenceequationwherethef0rwarddifference0perat0rAisdefinedbyAx.=xn 1-x.,{ri}2',isarealp0sitivesequence,ffN(n0)xR-Risc0ntinuousinxERf0reverynEN(no),xf(n,x)>Oforx/0,nEN(n0 1),N(s)isdefinedbyN(s)={s,s l,'-},seN(n0).Byasolution0f(E)wemeanarealsequence{I.}7',satisfying(E).Asolutionof(E)iscal1edn0n0scil1at0ry,ifitiseventua1lypositive0rnegative,otherwiseitiscalledoscillat0ry.Eq.(E)isca1led0scil1atoryifa11so1utions-of(E)are0scillat0ry.Definiti0n1Thefuncti… 相似文献
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We study an eigenvalue problem in R N which involves the p ‐Laplacian (p > N ≥ 2) and the nonlinear term has a global (p – 1)‐sublinear growth. The existence of certain open intervals of eigenvalues is guaranteed for which the eigenvalue problem has two nonzero, radially symmetric solutions. Some stability properties of solutions with respect to the eigenvalues are also obtained. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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Justino Sánchez 《Journal of Mathematical Analysis and Applications》2004,292(2):401-414
We establish a existence result of multiple positive solutions for a singular eigenvalue type problem involving the one-dimensional p-Laplacian. Furthermore, we obtain a nonexistence result of positive solutions by taking advantage of the internal geometric properties related to the problem. Our approach is based on the fixed point index theory and the fixed point theorem in cones. 相似文献
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