Nodal Solutions of the p-Laplacian with Sign-Changing Weight

  title={Nodal Solutions of the p-Laplacian with Sign-Changing Weight},
  author={Ruyun Ma and Xilan Liu and Jia Xu},
and Applied Analysis 3 (iii) the eigenfunction corresponding to μ k (p) has exactly k − 1 simple zeros in (0, 1). Remark 3. Using the Gronwall inequality, we can easily show that all zeros of eigenfunction corresponding to eigenvalue μ ] k (p) are simple. It is very known that T2 λ is completely continuous in C 1 [0, 1].Thus, the Leray-Schauder degree dLS(I−T 2 λ , B r (0), 0) is well-defined for arbitrary r-ball B r (0) and λ ̸ = μ k , k ∈ Z and ] ∈ {+, −}. Lemma 4. For r > 0, we have dLS (I… CONTINUE READING

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