MULTIPLE POSITIVE SOLUTIONS FOR A CLASS OF SEMIPOSITONE NEUMANN PROBLEMS WITH SINGULAR φ-LAPLACIAN

作者：Ma, Ruyun^*; Gao, Hongliang

来源：Acta Mathematica Scientia, 2017, 37(5): 1472-1482.

DOI：10.1016/S0252-9602(17)30085-1

• multiple positive solutions
• Neumann problem
• prescribed mean curvature equation
• time map

We study the existence of multiple positive solutions for a Neumann problem with singular phi-Laplacian @@@ {-(phi(u'))' = lambda f(u), x is an element of(0,1) @@@ u' (0) = 0 = u'(1), @@@ where lambda is a positive parameter, phi(s) = s/root 1-s(2), f is an element of c(1) (0,infinity),R), f'(u) > 0 for u > 0, and for some 0 < beta < theta such that f (u) < 0 for u is an element of [0, beta) (semipositone) and f (u) > 0 for u > beta. Under some suitable assumptions, we obtain the existence of multiple positive solutions of the above problem by using the quadrature technique. Further, if f is an element of C-2([0, beta) boolean OR (beta, infinity), R), f" (u) >= 0 for u is an element of [0, beta) and f"(u) <= 0 for u is an element of (beta, infinity), then there exist exactly 2n + 1 positive solutions for some interval of lambda, which is dependent on n and theta. Moreover, We also give some examples to apply our results.

• 出版日期2017-9
• 单位西北师范大学