| We will establish existence results for semilinear elliptic problems of the form Lu-au++bu-+gx, u=fx x∈W, u=0on6W , where O is a bounded domain in Rn with smooth boundary ∂O, L is an elliptic operator of second order in divergence form with C1-coefficients, g is a Caratheodory function satisfying certain growth conditions, and f belongs to Linfinity(O). We employ so-called Landesman-Lazer conditions as key ingredients for existence in the following resonance cases: (1) One-sided resonance at a Fucik eigenvalue from the first Fucik curve of L, i.e. (alpha,beta) belongs to that curve and alpha ≠ beta, and g has sublinear growth at infinity. (2) Double resonance between (lambda +,lambda-) and (lambda1,lambda 1) where lambda1 is the smallest (classical) eigenvalue of L and (lambda+,lambda-) belongs to the first Fucik curve of L. (3) General result of one-sided resonance at an arbitrary Fucik eigenvalue where g has sublinear growth at infinity. |
